Current Electricity · Physics · Class 12

Two wires $P$ and $Q$ are made of the same material. The wire $\mathbf{Q}$ has twice the diameter and half the length as that of wire $P$. If the resistance of wire $P$ is $R$, the resistance of the wire $Q$ will be

A battery supplies 0.9 A current through a $2 \Omega$ resistor and 0.3 A current through a $7 \Omega$ resistor when connected one by one. The internal resistance of the battery is

A galvanometer of resistance $50 \Omega$ is converted into a voltmeter of range $(0-2 \mathrm{~V})$ using a resistor of $1.0 \mathrm{k} \Omega$. If it is to be converted into a voltmeter of range ( $0-10 \mathrm{~V}$ ), the resistance required will be

A current of 0.8 A flows in a conductor of $$40 \Omega$$ for 1 minute. The heat produced in the conductor will be

A cell of emf $$E$$ is connected across an external resistance $$R$$. When current '$$I$$' is drawn from the cell, the potential difference across the electrodes of the cell drops to $$\mathrm{V}$$. The internal resistance '$$r$$' of the cell is

Assertion (A) : The equivalent resistance between points A and B in the given network is 2R.

Reason (R) : All the resistors are connected in parallel

A battery of emf $E$ and internal resistance $r$ is connected to a rheostat. When a current of 2 A is drawn from the battery, the potential difference across the rheostat is $\mathbf{5 ~ V}$. The potential difference becomes 4 V when a current of 4 A is drawn from the battery. Calculate the value of $E$ and $r$.

(a) Two batteries of emf's 3 V and 6 V and internal resistances $0.2 \Omega$ and $0.4 \Omega$ are connected in parallel. This combination is connected to a $4 \Omega$ resistor. Find:

(i) the equivalent emf of the combination

(ii) the equivalent internal resistance of the combination

(iii) the current drawn from the combination

OR

(b) (i) A conductor of length $l$ is connected across an ideal cell of emf $E$. Keeping the cell connected, the length of the conductor is increased to $2 l$ by gradually stretching it. If $R$ and $R^{\prime}$ are initial and final values of resistance and $v_d$ and $v_d{ }^{\prime}$ are initial and final values of drift velocity, find the relation between

(1) $R^{\prime}$ and $R$ and

(2) $v_d{ }^{\prime}$ and $v_d$.

(ii) When electrons drift in a conductor from lower to higher potential, does it mean that all the 'free electrons' of the conductor are moving in the same direction?

Briefly explain why and how a galvanometer is converted into an ammeter.

Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the conductor and relaxation time.

The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the conductor? Justify your answers.

(a) Briefly describe how the current sensitivity of a moving coil galvanometer can be increased.

(b) A galvanometer shows full scale deflection for current $$I_g$$. A resistance $$R_1$$ is required to convert it into a voltmeter of range $$(0-V)$$ and a resistance $$R_2$$ to convert it into a voltmeter of range $$(0-2 \mathrm{~V})$$. Find the resistance of the galvanometer.

(a) (i) Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence obtain an expression for it.

(ii) Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in $$\mathrm{A}$$ is 1.5 times that in $$\mathbf{B}$$. Find the ratio of drift velocity of electrons in wire A to that in wire. B.

OR

(b) (i) A cell emf of $$(\mathrm{E})$$ and internal resistance $$(\mathrm{r})$$ is connected across a variable load resistance (R). Draw plots showing the variation of terminal voltage $$V$$ with (i) $$R$$ and (ii) the current (I) in the load.

(ii) Three cells, each of emf $$\mathrm{E}$$ but internal resistances $$2 r, 3 r$$ and $$6 r$$ are connected in parallel across a resistor $$R$$.

Obtain expressions for (i) current flowing in the circuit, and (ii) the terminal potential difference across the equivalent cell.