Parameters and Performance of Transmission Lines · Power System Analysis · GATE EE

A 50 Hz, 275 kV line of length 400 km has the following parameters:

Resistance, R = 0.035 $$\Omega$$/km;

Inductance, L = 1 mH/km;

Capacitance, C = 0.01 $$\mu$$F/km;

The line is represented by the nominal-$$\pi$$ model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by $$V_S$$ and $$V_R$$, respectively) maintained at 275 kV, the phase angle difference ($$\theta$$) between $$V_S$$ and $$V_R$$ required for maximum possible active power to be delivered to the receiving end, in degree is ___________ (Round off to 2 decimal places).

The geometric mean radius of a conductor, having four equal strands with each strand of radius r, as shown in the figure below, is

In the figure, the voltages are

$${v_1}\left( t \right) = 100\cos \left( {\omega t} \right)$$

$${v_2}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {18}}} \right)$$

and $${v_3}\left( t \right) = 100\cos \left( {\omega t + {\pi \over {36}}} \right)$$.

The circuit is in sinusoidal steady state, and R << $${\omega L}$$. P₁, P₂ and P₃ are the average power outputs. Which one of the following statements is true?

The normal - $$\pi $$ circuit of a transmission line is shown in the figure.

Impedance $$Z = 100\angle {80^ \circ }$$ and reactance $$\,X = 3300\Omega .$$ The magnitude of the characteristic impedance of the transmission line, in $$\Omega ,$$ is ________. (Give the answer up to one decimal place.)

A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $$v_{an}=220\sin\left(100\mathrm{πt}\right)\;V$$ and $$i_a=10\sin\left(100\mathrm{πt}\right)\;A$$, respectively. Similarly for phase-b the instantaneous voltage and current are $$v_{bn}=220\cos\left(100\mathrm{πt}\right)\;V$$ and $$i_b=10\cos\left(100\mathrm{πt}\right)\;A$$, respectively. The total instantaneous power flowing form the source to the load is

In a long transmission line with $$r, l, g$$ and $$𝑐$$ are the resistance, inductance, shunt conductance and capacitance per unit length respectively, the condition for distortionless transmission is

A single phase induction motor draws $$12MW$$ power at $$0.6$$ lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of motor and capacitor to $$0.8$$ lagging. Assuming that the real and reactive power drawn by the motor remains same as before, the reactive power delivered by the capacitor in MVAR is _______ .

The undesirable property of an electrical insulating material is

A single load is supplied by a single voltage source. If the current flowing from the load to the source is $$10\angle - {150^0}$$ A and if the voltage at the load terminals is $$100\angle {60^0}$$ $$V,$$ then the

For enhancing the power transmission in along $$EHV$$ transmission line, the most preferred is to connect a

A nuclear power station of $$500$$ $$MW$$ capacity is located at $$300$$ km away from a load center. Select the most suitable power evacuation transmission configuration among the following options.

Consider two buses connected by an impedance of $$\left( {0 + j5} \right)\Omega .$$ The bus $$1$$ voltage is $$100$$$$\angle {30^ \circ }\,\,\,V,$$ and bus $$2$$ voltage is $$100\angle {0^ \circ }\,\,\,V,$$ The real and reactive power supplied by bus $$1,$$ respectively, are

Consider a step voltage wave of magnitude $$1$$ pu travelling along a loss less transmission line that terminates in a reactor. The voltage magnitude across the reactor at the instant the travelling wave reaches the reactor is

For a fixed value of complex power flow in a transmission line having a sending end voltage $$V$$, the real power loss will be proportional to

An extra high voltage transmission line of length $$300$$ km can be approximate by a lossless line having propagation constant $$\beta = 0.00127$$ radians per km. then the percentage ratio of line length to wavelength will be given by

Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer. Which of the following connections, and the corresponding phase shift $$\theta ,$$ should be used for the transformer between $$A$$ and $$B$$?

Consider a bundled conductor of an overhead line consisting of three identical sub-conductors placed at the corners of an equilateral triangle as shown in figure. If we neglect the charges on the other phase conductors and ground, and assume that spacing between sub-conductors is much larger than their radius, the maximum electric field intensity is experienced at

A $$400$$ V, $$50$$ Hz, three phase balanced source supplies power to a star connected load whose rating is $$12\sqrt 3 $$ kVA, $$0.8$$ pf(lag). The rating (in kVAR) of the delta connected (capacitive) reactive power bank neccessary to bring the pf to unity is

The concept of an electricity short, medium and long line is primarily based on the

The insulation strength of an EHV transmission line is mainly governed by

The phase sequence of the $$3$$-phase system shown in figure is

The rated voltage of a $$3$$-phase power system is given as

Total instantaneous power supplied by a $$3$$-phase ac supply to a balanced $$R$$-$$L$$ load is

Bundled conductors are mainly used in high voltage overhead transmission lines to

A $$3$$-phase, $$11$$-$$kV$$ generator feeds power to a constant power unity power factor load of $$100$$ $$MW$$ through a $$3$$-phase transmission line. The line-to-line voltage at the terminals of the machine is maintained constant at $$11$$ $$kV$$. The per unit positive sequence impedance of the line based on $$100$$ $$MVA$$ and $$11$$ $$kV$$ is $$j$$ $$0.2$$. The line to line voltage at the load terminals is measured to be less than $$11$$ $$kV$$. The total reactive power to be injected at the terminals of the load to increase the line-to-line voltage at the load terminals to $$11$$ $$kV$$ is

Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is $$0.25$$ cm and the distance between their centers is $$1$$m. If this distance is doubled, then the inductance per unit length.

A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at

A lossless radial transmission line with surge impedance loading

The load carrying capability of a long AC transmission line is

Corona losses are minimized when

An overhead line having a surge impedance of $$400$$$$\Omega $$ is connected in series with an underground cable having a surge impedance of $$100$$$$\Omega $$. If a surge of $$50$$ $$kV$$ travels from the line end towards the cable junctions, the value of the transmitted voltage wave at the junction is

Series capacitive compensation in $$EHV$$ transmission lines is used to

The reflection coefficient for the transmission line shown in figure at $$P$$ is

For a $$500$$ Hz frequency excitation, a $$50$$ km short power line will be modeled as

The insulation resistance of a cable of length $$10$$ km is $$1$$ $$M\Omega $$. For a length of $$100$$ km of the same cable, the insulation resistance will be

The surge impedance of a $$400$$ km long overhead transmission line is $$400$$ $$\Omega $$. For a $$200$$ km length of the same line, the surge impedance will be

The insulation level of a $$400$$ kV, EHV overhead transmission line is decided on the basis of

In a $$400$$ kV network, $$360$$ kV is recorded at a $$400$$ kV bus. The reactive power absorbed by a shunt reactor rated for $$50$$ MVAR, $$400$$ kV connected at the bus is

A three phase overhead transmission line has its conductors horizontally spaced with spacing between adjacent conductors equal to 'd'. If now the conductors of the line are rearranged to form an equilateral triangle of sides equal to 'd' then

The selection of size of conductors for a distributor in a distribution system is governed by

The inductance of a power transmission line increases with

Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G₁ and G₂ are Q_G1 and Q_G2 respectively. The per unit values of Q_G1, Q_G2, and line reactive power loss (Q_loss) respectively are

Consider an overhead transmission line with $$3$$-phase, $$50$$ $$Hz$$ balanced system with conductors located at the vertices of an equilateral triangle of length $$\,{D_{ab}} = {D_{bc}} = {D_{ca}} = 1\,\,\,$$ m as shown in figure below. The resistance of the conductors are neglected. The geometric mean radius (GMR) of each conductor is $$0.01$$ $$m$$. Neglect the effect of ground, the magnitude of positive sequence reactance in $$\,\Omega $$/$$km$$ (rounded off to three decimal places) is ________________.

A 3-phase 50 Hz generator supplies power of 3 MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25 $$\Omega $$ and 3.925 $$\Omega $$ respectively. If the voltage at the generator terminal is 17.87 kV, the power factor of the load is ________.

A load is supplied by a $$230$$ $$V,$$ $$50$$ $$Hz$$ source. The active power $$P$$ and the reactive power $$Q$$ consumed by the load are such that $$1$$ $$kW$$ $$ \le P \le 2\,kW\,\,$$ and $$\,1\,\,kVAR \le 2\,\,kVAR.\,\,$$ A capacitor connected across the load for power factor correction generates $$1$$ $$kVAR$$ reactive power. The worst case power factor after power factor correction is

A three-phase cable is supplying $$800$$ kW and $$600$$ kVAr to an inductive load. It is intended to supply an additional resistive load of $$100$$ kW through the same cable without increasing the heat dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the load. Given the line voltage is $$3.3$$ kV, $$50$$ Hz, the capacitance per phase of the bank expressed in microfarads, is ________.

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ________.

A composite conductor consists of three conductors of radius $$R$$ each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kR. The value of k is ______.

The complex power consumed by a constant-voltage load is given by $$\left( {{P_1} + {J_{q1}}} \right).\,\,$$ Where, $$\,1\,\,kW \le \,\,{P_1} \le \,\,\,1.5\,\,kW\,\,\,$$ and $$\,\,0.5\,KVAR \le \,\,\,{Q_1} \le 1kVAR.\,\,\,$$ A compensating shunt capacitor is chosen such that $$\,\left| Q \right| \le 0.25\,\,KVAR,\,\,$$ where $$Q$$ is the net reactive power consumed by the capacitor-load combination. The reactive power (in kVAR) supplied by the capacitor is ____________.

For a $$400$$ $$km$$ long transmission line, the series impedance is $$(0.0 + j0.5)$$ $$\Omega /km$$ and the shunt admittance is $$(0.0 + j5.0)$$ $$\mu \,mho/km.$$ The magnitude of the series impedance (in $$\Omega $$) of the equivalent $$\pi $$ circuit of the transmission line is __________.

The horizontally placed conductors of a single phase line operating at $$50$$ $$Hz$$ are having outside diameter of $$1.6$$ cm, and the spacing between centers of the conductors is $$6$$ m. The permittivity of free space is $$8.854 \times {10^{ - 12}}\,\,F/m.$$ The capacitance to ground per kilometer of each line is

A distribution feeder of $$1$$ $$km$$ length having resistance, but negligible reactance, is fed from both the ends by $$400$$ $$V,$$ $$50$$ $$Hz$$ balanced sources. Both voltage sources $${S_1}$$ and $${S_2}$$ are in phase. The feeder supplies concentrated loads of unity power factor as shown in the figure.

The contributions of $${S_1}$$ and $${S_2}$$ in $$100$$ $$A$$ current supplied at location $$P$$ respectively, are

A two bus power system shown in figure supplies load of $$1.0+j0.5$$ $$p.u$$

The value of $${V_1}$$ in $$p.u$$ and $${\delta _2}$$ respectively are

For the system shown below, S_D1 and S_D2 are complex power demands at bus $$1$$ and bus $$2$$ respectively. If $$\left| {{V_2}} \right| = 1$$ pu, the VAR rating of the capacitor (Q_G2) connected at bus $$2$$ is

A lossy capacitor $${C_x}$$, rated for operation at $$5$$ $$kV,$$ $$50$$ $$Hz$$ is represented by an equivalent circuit with an ideal capacitor $${C_p}$$ in parallel with a resistor $${R_p}$$. The value $${C_p}$$ is found to be $$0.102$$ $$\mu F$$ and the value of $${R_p}$$ $$=$$ $$1.25$$ $$M\Omega .$$ Then the power loss and $$tan\delta $$ of the lossy capacitor operating at the rated voltage, respectively, are

A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator?

Consider a three-phase, $$50Hz,$$ $$11$$ $$kV$$ distribution system. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The self capacitance of the insulator is $$5$$ times the shunt capacitance between the link an the ground, as shown in the figure. The voltage across the two insulators are

Consider a three-core, three phase, $$50$$ $$Hz$$, $$11$$ $$kV$$ cable whose conductors are denoted as $$R, Y$$ and $$B$$ in the figure. The inter-phase capacitance $$\left( {{C_1}} \right)$$ between each pair of conductors is $$0.2$$ $$\mu F$$ and the capacitance between each line conductor and the sheath is $$0.4$$ $$\mu F$$ . The per-phase charging current is

Match the items List-$${\rm I}$$ (To) with the items in List-$${\rm II}$$ (Use) and select the correct answer using the codes given below the lists.

List-$${\rm I}$$
$$A.$$ improve power factor
$$B.$$ reduce the current ripples
$$C.$$ increase the power flow in line
$$D$$ reduce the Ferranti effect

List-$${\rm II}$$
$$1.$$ shunt reactor
$$2.$$ shunt capacitor
$$3.$$ series capacitor
$$4.$$ series reactor

A lossless transmission line having Surge Impedance Loading $$(SIL)$$ of $$2280$$ $$MW.$$ A Series capacitive compensation of $$30$$% is emplaced. Then $$SIL$$ of the compensated transmission line will be

Single line diagram of a $$4$$-bus single source distribution system is shown below. Branches $${e_1},\,\,$$ $${e_2},\,\,$$ $${e_3}\,\,$$ and $${e_4}\,\,$$ have equal impedences. The load current values indicated in the figure are in per unit.

Distribution Company's policy requires radial system operation with minimum loss. This can be achieved by opening of the branch

$$230$$ $$V$$ (phase) $$50$$ Hz, three-phase, $$4$$-wire, system has a sequence $$ABC$$. A unity power-factor load of $$4$$ kW is connected between phase A and neutral $$N$$. It is desired to achieve zero neutral current through the use of a pure inductor and pure capacitor in the other two phases. The Value of inductor and capacitor is......

The total reactance and total susceptance of a lossless overhead $$EHV$$ line, operating at $$50$$ $$Hz,$$ are given by $$0.045$$ pu and $$1.2$$ pu respectively. If the velocity of wave propagation is $$3\,\, \times \,\,{10^5}$$ km/s, then the approximate length of line is

The $$A, B, C, D$$ constant of a $$220$$ $$kV$$ line are:
$$A = D = 0.94\,\angle \,10,\,\,\,B = 130\,\angle \,730,\,\,\,C = 0.001\,\angle \,900.\,\,$$ If the sending end voltage of the line for a given load delivered at nominal voltage is $$240$$ $$kV$$, the % voltage regulation of the line is

At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power factor at $$0.97$$ lagging. If the capacitor goes out of service, the load power factor becomes

A lightning stroke discharges impulse current of $$10$$ kA (peak) on a $$400$$ kV transmission line having surge impedance of $$250\,\Omega $$. The magnitude of transient over-voltage traveling waves in either direction assuming equal distribution form the point of lightning strike will be

A $$110$$ $$kV,$$ single core coaxial, XLPE insulated power cable delivering power at $$50$$ $$Hz,$$ has a capacitance of $$125$$ $$nF/km.$$ If the dielectric loss tangent of XLPE is $$\,2\,\, \times \,\,{10^{ - 4}},$$ the dielectric power loss in this cable in $$W/km$$ is

A $$800$$ $$kV$$ transmission line is having per phase line inductance of $$1.1$$ $$mH/km$$ and per phase line capacitance of $$11.68$$ $$nF/km.$$ Ignoring the length of the line, its ideal power transfer capability in $$MW$$ is

The generalized circuit constants of a $$3$$-phase, $$220$$ $$kV$$ rated voltage, medium length transmission line are $$A = D = 0.936 + j\,0.016 = 0.936\angle {0.98^ \circ }$$
$$B = 33.5 + j138 = 142.0\angle {76.4^ \circ }\,\Omega $$
$$\,C = \left( { - 5.18 + j914} \right) \times \,{10^{ - 6}}\,\Omega $$
If the load at the receiving end is $$50$$ MW at $$220$$ $$kV$$ with a power factor of 0.9 lagging, then magnitude of line to line sending end voltage should be

The ABCD parameters of a $$3$$-phase overhead transmission line are $$\,A = D = 0.9\angle {0^ \circ }.\,\,B = 200\,\angle {90^ \circ }\,\,\Omega \,\,\,$$ and $$\,\,C = 0.95\, \times \,\,{10^{ - 3}}\angle {90^ \circ }\,\,S.\,\,\,\,$$ At no-load condition, a shunt inductive reactor is connected at the receiving end of the line to limit the receiving end voltage to be equal to the sending-end voltage. The ohmic value of the reactor is

A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the cable are 0.4 mH and 0.5 $$\mu F$$ per km. The inductance and capacitance of the overhead transmission lines are 1.5 mH and 0.015 $$\mu F$$ per km. The magnitude of the voltage at the junction due to surge is

A dc distribution system is shown in figure with load currents as marked. The two ends of the feeder are fed by voltage sources such that $${V_P} - {V_Q} = 3V.$$ the value of the voltage $${V_P}$$ for a minimum voltage of $$220$$ $$V$$ at any point along the feeder is

A balanced delta connected load of $$\left( {8 + j6} \right)\Omega $$ per phase is connected to a $$400$$ $$V$$, $$50$$ $$Hz$$, $$3-$$phase supply lines. If the input power factor is to be improved to $$0.9$$ by connecting a bank of star connected capacitors the required KVAR of the bank is

The conductors of a $$10$$ km long, single phase, two wire line are separated by a distance of $$1.5$$ m. The diameter of each conductor is $$1$$ cm. If the conductors are of copper, the inductance of the circuit is

Consider the model shown in figure of a transmission line with a series capacitor at its mid-point. The maximum voltage on the line is at the location

The corona loss on a particular system at 50 Hz is 1 kW/km per phase. The corona loss at 60 Hz would be

A transmission line has equal voltages at the two ends, maintained constant by two sources. A third source is to be provided to maintain constant voltage (equal to end voltages) at either the midpoint of the line or at $$75$$% of the distance from the sending end. Then the maximum power transfer capabilities of the line in the original case and the other two cases respectively will be in the following ratios.

A 3-phase, 11 kV, 50 Hz, 200 kW load has a power factor of 0.8 lag. A delta connected 3-phase capacitor is used to improve the power factor to unity. The capacitance power phase of the capacitor in micro-farads is

A single phase AC distributor supplies two single phase loads as shown in figure. The voltage drop from A to C is

$$A$$ $$220$$ kV, $$20$$ km long, $$3$$-phase transmission line has the following $$A, B, C, D$$ constants. $$A=D=0.96$$$$\angle {3^0},$$ $$\,B = 55\angle {65^0}\,\,\Omega /$$ phase, $$\,C = 0.5 \times {10^{ - 4}}\angle {90^0}\,\,$$ $$S/$$phase. Its correct charging current per phase is

For a single phase overhead line having solid copper conductors of diameter $$1$$ cm, spaced $$60$$ cm between centers, the inductance in $$mH/km$$ is

A cable has the following characteristics. $$L = 0.201\,\,\mu H/m\,\,$$ and $$\,C = 196.2\,pF/m.\,$$ The velocity of wave propagation through the cable is

A shunt reactor of $$100$$ MVAR is operated at $$98$$% of its rated voltage and $$96$$% of its rated frequency. The reactive power absorbed by the reactor is;

For equilateral spacing of conductors of an untransposed $$3$$-phase line, we have

The rated load of an underground cable is always _______its natural load.

The charging current of a $$400$$ kV transmission line is more than that of a $$220$$ kV line of the same length.

Consider a three-phase, $$50$$ $$Hz$$, $$11$$ $$kV$$ distribution system. Each of the conductors is suspended by an insulator string having two identical porcelain insulators. The self capacitance of the insulator is $$5$$ times shunt capacitance. The voltage drop across botton most disc is:

In a transmission line each conductor is at $$20$$ $$kV$$ and is supported by a string of $$3$$ suspension insulators. The air capacitance between each cap-pin junction and tower is one-fifth of the capacitance $$C$$ of each insulation unit. A guard ring, effective only over the line-end insulator unit is fitted so that the voltages on the two units nearest the line-end are equal.

(a) Calculate the voltage on the line-end unit.
(b) Calculate the value of capacitance $${C_x}$$ required.

A long lossless transmission line has a unity power factor (UPF) load at the receiving end and an ac voltage source at the sending end. The parameters of the transmission line are as follows:
Characteristic impedance $${Z_c} = 400\Omega ,\,\,$$, propagation constant $$\,\beta = 1.2 \times {10^{ - 3}}\,\,rad/km,\,\,$$ and length $$\,l = 100\,km.\,\,$$ The equation relating sending and receiving end questions is $${V_s} = {V_r}\,\cosh \,\,\left( {\beta l} \right) + j\,Z{}_c\,\,\sinh \left( {\beta l} \right){{\rm I}_R}$$ Complete the maximum power that can be transferred to the UPF load at the receiving end if $$\left| {{V_s}} \right| = 230\,\,kV.\,\,$$

A 132 kV transmission line AB is connected to a cable BC. The characteristic impedances of the overhead line and the cable are 400$$\Omega $$ and 80$$\Omega $$ respectively. Assume that these are purely resistive. A 250 kV switching surge travels from A to B.

(a) Calculate the value of this voltage surge when it first reaches C.

(b) Calculate the value of the reflected component of this surge when the first reflection reaches A.

(c) Calculate the surge current in the cable BC.

A $$275$$ $$kV,$$ $$3$$-phase, $$50$$ $$Hz,$$ $$400$$ $$km$$ lossless line has following parameters:
$$x=0.05$$ $$ohms/km,$$ line charging susceptance $$y=3.0$$ micro-Siemens/k.

(a) Calculate the receiving end voltage on open circuit using justifiable assumptions.

(b) What load at the receiving end will result in a flat voltage profile on the line?

(c) If the flat voltage profile is to be achieved at $$1.2$$ times the loading in (b), what will be the nature and quantum of uniformly distributed compensation required?

A 66 kV, 3-phase, 50 Hz, 150 km long overhead transmission line is open circuited at the receiving end. Each conductor has a resistance of 0.25$$\Omega $$/km, an inductive reactance of 0.5$$\Omega $$/km and a capacitive admittance to neutral of 0.04 $$ \times $$ 10^-4 S/km.

(a) Draw the nominal π-equivalent circuit and indicate the value of each parameter.
(b) Calculate the receiving end voltage if the sending end voltage is 66 kV.

A 6.6 kV, 50 Hz single core lead sheathed cable has the following data:
Conductor diameter: 1.5 cm, length: 4 km. Internal diameter of the sheath : 3 cm
Resistivity of insulation : 1.3 $$ \times $$ 1012 $$\Omega $$-m. Relative permittivity of insulation : 3.5 Calculate

(a) the insulation resistance
(b) the capacitance and
(c) the maximum electric stress in the insulation

Each conductor of a $$33$$ $$kV,$$ $$3$$ phase system is suspended by a string of three similar insulators. The ratio of shunt capacitance to mutual capacitance is $$0.1.$$ Calculate the voltage across each insulator, and the string efficiency.

A factory draws $$100$$ kW at $$0.7$$ p.f. lagging from a $$3$$-phase, $$11$$ kV supply. It is desired to the p.f. to $$0.95$$ lagging using series capacitors. Calculate the rating of the capacitor required.

The increase in resistance due to non-uniform distribution of current in a conducto $$r$$ is known as _______effect