Q. A cylindrical copper rod is reformed to twice its original length with no change in volume. The resistance between its ends before the change was $R$. Now its resistance will be :

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A

$8 R$

B

$6 R$

C

$4 R$

D

$2 R$

Solution:

As length is increased to double that means for the constant volume its cross sectional area will decrease to half so its resistance will become four times.

Questions from Current Electricity

1. Two sources of equal emf are connected to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2 (R_2 > R_1).$ If the potential difference across the source having internal resistance $R_2$, is zero, then :

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2. In the network shown in figure, each resistance is equal to $2 \Omega$. The resistance between the points $A$ and $B$ is

3. A letter ' $A$ ' is constructed from a uniform wire with resistance $1.0\, \Omega$ per $cm .$ The sides of the letter are $20\, cm$ and the cross piece in the middle is $10\, cm$ long. The apex angle is $60^{\circ} .$ The resistance between the ends of the legs is

4. The diagrams show five different ways in which currents $i_{1}, i_{2}, i_{3}$ can combine at a junction.

For which of these junctions, is the following equation correct ?
$i_{1}+i_{2}=i_{3}+i_{4}$

5. A battery of emf, $10\, V$ is connected to resistances as shown in figure. The potential difference $V_{A}-V_{B}$ between the points $A$ and $B$ is

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1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

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2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

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3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

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4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

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5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

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