Resistance and Resistors

Q.

Explain what you understand by temperature coefficient.

Q.

The potential difference between A and B in the following figure is:

1. $48V$

2. $32V$

3. $24V$

4. $14V$

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. In the circuit shown in the figure, the reading of the voltmeter $V$ will be

1. $4\text{V}$
2. $2\text{V}$
3. $6\text{V}$
4. $3\text{V}$

Q. Internal resistance of a $2.1V$ cell which gives a current of 0.2 A through an external resistance of $10\Omega$ is

1. $0.2\Omega$
2. $0.5\Omega$
3. $0.8\Omega$
4. $1.0\Omega$

Q. $n$ identical cells, each of emf $\text{E}$ and internal resistance $r$, are joined in series to form a closed circuit. One of the cells is joined with reversed polarity. The potential difference across each cell, except the cell with the reversed polarity, is -

1. $\frac{2\text{E}}{n}$
2. $\left(\frac{n-1}{n}\right)\text{E}$
3. $\left(\frac{n-2}{n}\right)\text{E}$
4. $\left(\frac{2n}{n-2}\right)\text{E}$

Q. In the circuit shown, the potential difference between $A$ and $B$ is :

1. $1\text{V}$
2. $2\text{V}$
3. $3\text{V}$
4. $6\text{V}$

Q. Two batteries of emf $4\text{V}$ and $8\text{V}$ with internal resistances $1\Omega$ and $2\Omega$ are connected in a circuit with a resistance of $9\Omega$ as shown in figure. The current and potential difference between the points $\text{P}$ and $\text{Q}$ are

1. $\frac{1}{3}\text{A}$ and $3\text{V}$
2. $\frac{1}{6}\text{A}$ and $4\text{V}$
3. $\frac{1}{9}\text{A}$ and $9\text{V}$
4. $\frac{1}{2}\text{A}$ and $12\text{V}$

Q. What equal length of an iron wire and a copper-nickel alloy wire, each of $2\text{mm}$ diameter connected parallel to give an equivalent resistance of $3\Omega$ ?
(Given resistivities of iron and copper-nickel alloy wire are $12\mu \Omega \text{cm}$ and $51\mu \Omega \text{cm}$ respectively)

1. $110\text{m}$
2. $82\text{m}$
3. $97\text{m}$
4. $90\text{m}$

Q. In the given circuit, potential of junction A is

1. 1.73 V
2. 3.82 V
3. 2.5 V
4. 4 V

Q.

A conducting wire of length $l$, area of cross-section $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be:

1. $\frac{1}{4}\frac{\rho l}{VA}$

2. $\frac{3}{4}\frac{VA}{\rho l}$

3. $4\frac{VA}{\rho l}$

4. $\frac{1}{4}\frac{VA}{\rho l}$

Q. The resistance of a conductor at ${15}^{\circ }C$ is $16\Omega$ and at ${100}^{\circ }C$ is $20\Omega$. What will be the temperature coefficient of resistance of the conductor?

1. ${0.010}^{\circ }{C}^{-1}$
2. ${0.033}^{\circ }{C}^{-1}$
3. ${0.003}^{\circ }{C}^{-1}$
4. ${0.042}^{\circ }{C}^{-1}$

Q. The potential difference between points $\text{A}$ and $\text{B}$ in the circuit shown in figure will be

1. $1\text{V}$
2. $2\text{V}$
3. $-3\text{V}$
4. $-\frac{40}{9}\text{V}$

Q. The resistance of a wire is $4.2\Omega$ at ${100}^{\circ }C$ and the temperature coefficient of the material is $0.004{/}^{\circ }C$. Its resistance at $0^{\circ }C$ is

1. $2.5\Omega$
2. $3\Omega$
3. $5\Omega$
4. $6\Omega$

Q. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3\%$ each, then percentage error in the value of resistance of wire is:

1. $6\%$
2. $zero$
3. $1\%$
4. $3\%$

Q.

Two resistance $R_1$ and $R_2$ are made of different materials. The temperature coefficient of the material of $R_1$ is $\alpha$ and that of the material of $R_2$ is $\beta$ . The resistance of the series combination of $R_2$ and $R_1$ does not change with temperature, then the ratio of resistances of the two wires at $0^o$ will be:

1. $\frac{\alpha +\beta }{\alpha -\beta }$
2. $\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }$
3. $\frac{\beta }{\alpha }$
4. $\frac{2\alpha }{\beta }$

Q. A wire of resistance 5 ohm is drawn out so that its new length is three times its original length. What is the resistance of the new wire ?

1. $\frac{5}{3}\Omega$
2. $5\Omega$
3. $15\Omega$
4. $45\Omega$

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

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. The four arms of a wheatstone bridge have resistances as shown in the figure. A galvanometer of $15\Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10\text{V}$ is maintained across $AC$.

1. $4.87\text{mA}$
2. $4.87\mu \text{A}$
3. $2.44\mu \text{A}$
4. $2.44\text{mA}$

Q. A wire of length 5m and radius 1mm has a resistance of 1 ohm. What length of the wire of the same material at the same temperature and of radius 2mm will also have a resistance of 1 ohm

1. 20 m
2. 10 m
3. 1.25 m
4. 2.5 m

Q. A uniform wire of resistance $72\Omega$ is bent in the form of a hexagon (regular), then the effective resistance between A & B is

1. $10\Omega$
2. $9\Omega$
3. $6\Omega$
4. $8\Omega$

Q. Figure represents a part of closed circuit. The potential difference $(V_A-V_B)$ is:

1. $10\text{V}$
2. $13\text{V}$
3. $15\text{V}$
4. $18\text{V}$

Q. Find the resistance across points $A$ and $B$.

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

Q.

A rod of length L and cross-section area A lies along the x-axis between x = 0 and x = L. The material obeys Ohm's law and its resistivity varies along the rod according to $\rho \left(x\right)={\rho }_0{e}^{-x/L}$. The total resistance of the rod is

1. $\frac{{\rho }_{0}L}{A}\left(e\right)$

2. $\frac{{\rho }_{0}L}{A}(1-\frac{1}{e})$

3. $\frac{{\rho }_{0}L}{A}(e-1)$

4. $\frac{{\rho }_{0}L}{A}\left(\frac{1}{e}\right)$

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. Two resistors of resistances $200\text{k}\Omega$ and $1\text{M}\Omega$, respectively from a potential divider with outer junctions maintained at potentials of $+3\text{V}$ and $-15\text{V}$. What is the potential at the junction $\text{X}$ between the resistors?

1. $+1\text{V}$
2. $0\text{V}$
3. $-0.6\text{V}$
4. $-12\text{V}$

Q. A finite square grid with each link having resistance $r$ is fitted in a resistanceless conducting circular wire. The equivalent resistance between $\text{A}$ and $\text{B}$ will be:
$($Given, $r=80/7\Omega )$

1. $6\Omega$
2. $8\Omega$
3. $12\Omega$
4. $15\Omega$

Q. An aluminum rod and a copper rod are taken such that their lengths and resistance are same .The specific resistance of copper is half that of aluminum but its density is three times that of aluminum. The ratio of the mass of aluminum rod and that of copper rod will be

1. $\frac{1}{3}$
2. $\frac{1}{6}$
3. $\frac{2}{3}$
4. $6$

Q. A hollow cylinder $(\rho =2.2\times {10}^{-8}\Omega m)$ of length 3 m has inner and outer diameter as 2 mm and 4 mm respectively. The resistance of the cylinder is

1. $2217\times {10}^{-3}\Omega$
2. $0.35\times {10}^{-3}\Omega$
3. $3\times {10}^{-3}\Omega$
4. $7\times {10}^{-3}\Omega$