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1

AIEEE 2004

MCQ (Single Correct Answer)
Time taken by a $$836$$ $$W$$ heater to heat one litre of water from $$10{}^ \circ C$$ to $$40{}^ \circ C$$ is
A
$$150$$ $$s$$
B
$$100$$ $$s$$
C
$$50$$ $$s$$
D
$$200$$ $$s$$

Explanation

$$\Delta Q = mC \times \Delta T$$

$$ = 1 \times 4180 \times \left( {40 - 10} \right) = 80 \times 30$$

( $$\therefore$$ $$\Delta Q = $$ heat supplied in time $$t$$ for heating $$1L$$ water from $${10^ \circ }C$$ to $${40^ \circ }C$$ )

also $$\Delta Q = 836 \times t \Rightarrow t = {{4180 \times 30} \over {836}} = 150\,s$$
2

AIEEE 2004

MCQ (Single Correct Answer)
The total current supplied to the circuit by the battery is
A
$$4A$$
B
$$2A$$
C
$$1A$$
D
$$6A$$

Explanation



hence $${{\mathop{\rm R}\nolimits} _{eq}} = 3/2;$$

$$\therefore$$ $$I = {6 \over {3/2}} = 4A$$
3

AIEEE 2004

MCQ (Single Correct Answer)
An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii are in the ratio of $${4 \over 3}$$ and $${2 \over 3}$$, then the ratio of the current passing through the wires will be
A
$$8/9$$
B
$$1/3$$
C
$$3$$
D
$$2$$

Explanation



$${i_1}{R_1} = {i_2}{R_2}\,\,\,\,\,\,\,\,\,\,$$ (same potential difference)

V = I1R1 = I1$$ \times $$$${{\rho {l_1}} \over {\pi r_1^2}}$$

Also V = I2R2 = I2$$ \times $$$${{\rho {l_2}} \over {\pi r_2^2}}$$

$$ \therefore $$ I1$$ \times $$$${{\rho {l_1}} \over {\pi r_1^2}}$$ = I2$$ \times $$$${{\rho {l_2}} \over {\pi r_2^2}}$$

$$ \Rightarrow $$ $${{{I_1}} \over {{I_2}}} = {{{\ell _1}} \over {{\ell _2}}} \times {{r_1^2} \over {r_2^2}}$$

$$ = {3 \over 4} \times {4 \over 9} = {1 \over 3}\,\,$$
4

AIEEE 2004

MCQ (Single Correct Answer)
The resistance of the series combination of two resistances is $$S.$$ When they are jointed in parallel the total resistance is $$P.$$ If $$S = nP$$ then the Minimum possible value of $$n$$ is
A
$$2$$
B
$$3$$
C
$$4$$
D
$$1$$

Explanation



$$S = {R_1} + {R_2}$$ and $$P = {{{R_1}{R_2}} \over {{R_1} + {R_2}}}$$

$$S = nP \Rightarrow {R_1} + {R_2} = {{n\left( {{R_1}{R_2}} \right)} \over {\left( {{R_1} + {R_2}} \right)}}$$

$$ \Rightarrow {\left( {{R_1} + {R_2}} \right)^2} = n{R_1}{R_2}$$

$$ \Rightarrow n = {{R_1^1 + R_2^2 + {R_1}{R_2}} \over {{R_1}{R_2}}}$$

$$n = {{{R_1}} \over {{R_2}}} + {{{R_2}} \over {{R_1}}} + 2$$

Arithmetic mean $$ > $$ Geometric mean

Minimum value of $$n$$ is $$4$$

Questions Asked from Current Electricity

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