Resistance and Resistors

Q. In the given circuit, the value of current in different branches and one resistor are shown. The potential at point $B$ with respect to the point $A$ is

1. $+1\text{V}$
2. $-1\text{V}$
3. $+2\text{V}$
4. $-2\text{V}$

Q. The resistance of a wire is $R\Omega$ . If it is melted and stretched to $n$ times its original length, its new resistance will be

1. $\frac{R}{n^2}$
2. $nR$
3. $\frac{R}{n}$
4. $n^{2}R$

Q. Find the resistance of a hollow cylinder of inner radius 'a' and outer radius b chose ends are connected to a potential difference E. ($\rho$: resistivity).

1. $\frac{\rho l}{\pi a^2}$
2. $\frac{\rho l}{\pi b^2}$
3. $\frac{\rho l}{\pi (b^2-a^2)}$
4. None

Q. We know resistance is given by the equation,
$R=\frac{\rho l}{A}$
So, for a resistor of a particular material, if the resistance is doubled, by what factor does $\rho$ change?

1. 2
2. 1
3. 4
4. $\frac{1}{2}$

Q.

Find the $\%$ change in resistance if length is decreased by $3\%$ and radius is increased by $1.5\%$.

1. no change
2. $+2\%$
3. $-2\%$
4. $-6\%$

Q. The resistivity of a resistor is 5 ohm-m. Its length is 1m and area of cross section is $2m{m}^2$. Find the resistance?

1. $2M\Omega$
2. $2.5M\Omega$
3. $4M\Omega$
4. $5M\Omega$

Q. A wire of length L and resistance R is streched to get the radius of cross-section halved. What is the new resistance of the wire?

1. 5 R
2. 8 R
3. 4 R
4. 16 R

Q. The electrical resistance of a mercury column in a cylindrical container is $R$. When all of the mercury is poured out into another cylindrical container of half the radius of cross section, the resistance of the new mercury column will be ______.

1. $2R$
2. $4R$
3. $8R$
4. $16R$

Q. Four conductors of the same resistance are connected to form a square. If the resistance between diagonally opposite corners is $8\Omega$, the resistance between any two adjacent corners would be _____.

1. $32\Omega$
2. $8\Omega$
3. $\frac{1}{6}\Omega$
4. $6\Omega$

Q. Find the change in resistance if length is increased by $2\%$ and area is decreased by $1\%$

1. $+3\%$
2. $-3\%$
3. No change
4. $-2\%$

Q.

A resistance wire of 6$\Omega$ is cut into four equal parts . What is the resistance of each part?

Q. The specific resistance of a wire is $\rho$, its volume is $3m^3$ and its resistance is $3$ohms, then its length will be

1. $\sqrt{\frac{1}{\rho }}$
2. 3$\sqrt{\frac{1}{\rho }}$
3. $\frac{1}{\rho }\sqrt{3}$
4. $\rho \sqrt{\frac{1}{3}}$

Q. A wire is stretched so as to change its diameter by $0.25\%$. The percentage change in resistance is

1. $4\%$
2. $2\%$
3. $1\%$
4. $0.5\%$

Q. A wire of length L and resistance R is streched to get the radius of cross-section halved. What is the new resistance of the wire?

1. 5 R
2. 8 R
3. 4 R
4. 16 R

Q. In the circuit shown in figure, find the potential of $B$ and the current through $1\Omega$ resistance.

1. $3\text{V},7.5\text{A}$
2. $2\text{V},3\text{A}$
3. $15\text{V},3\text{A}$
4. $5\text{V},7.5\text{A}$