Series and Parallel Combination of Resistors

Q. Two uniform wires A and B are of the same metal and have equal masses. The radius of wire A is twice that of wire B. The total resistance of A and B when connected in parallel is

1. $4\Omega$ when the resistance of wire A is $4.25\Omega$
2. $5\Omega$ when the resistance of wire A is $4\Omega$
3. $4\Omega$ when the resistance of wire B is $4.25\Omega$
4. $5\Omega$ when the resistance of wire B is $4\Omega$

Q. In the circuit shown, the reading of ammeter is $2\text{A}$. The ammeter has negligible resistance. The value of $R$ equals

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

Q. Find the equivalent resistance between A and E (Resistance of each resistor is R).

1. $\frac{7}{12}R$
2. $\frac{7}{13}R$
3. $\frac{7}{15}R$
4. $\frac{7}{13}R$

Q. In the circuit given, $E=6.0V,R_1=100\Omega ,R_2=R_3=50\Omega$ and $R_4=75\Omega$. The equivalent resistance of the circuit $\left(\text{in}\Omega \right)$ is

1. $11.875$
2. $26.31$
3. $118.75$
4. None of these

Q. What will be the equivalent resistance of circuit shown in figure between two points A and D?

1. $10\Omega$
2. $20\Omega$
3. $30\Omega$
4. $40\Omega$

Q. In the circuit shown in the figure, find the current in $45\Omega$.

1. $4\text{A}$
2. $2.5\text{A}$
3. $2\text{A}$
4. $\text{none}$

Q. The potential difference between points A and B of adjoining figure is -

1. $\frac{2}{3}$ V
2. $\frac{8}{9}$ V
3. $\frac{4}{3}$ V
4. 2 V

Q. Nine resistors each of resistance R are connected in the circuit as shown in figure. The effective resistance between A and B is

1. $\frac{7}{6}R$
2. $R$
3. $\frac{3}{5}R$
4. $\frac{2}{9}R$

Q. A wire of resistor R is bent into a circular ring of radius r. Equivalent resistance between two points X and Y on its circumference, when angle XOY is $\alpha$, can be given by

1. $\frac{R\alpha }{4{\pi }^2}(2\pi -\alpha )$
2. $\frac{R}{2\pi }(2\pi -\alpha )$
3. $R(2\pi -\alpha )$
4. $\frac{4\pi }{R\alpha }(2\pi -\alpha )$

Q. The effective resistance between points P and Q of the electrical circuit shown in figure is

1. $\frac{2Rr}{(R+r)}$
2. $8R\frac{(R+r)}{(3R+r)}$
3. 2r + 4R
4. $\frac{5R}{2+2r}$

Q. The effective resistance between points P and Q of the electrical circuit shown in figure is

1. $\frac{2Rr}{(R+r)}$
2. $8R\frac{(R+r)}{(3R+r)}$
3. 2r + 4R
4. $\frac{5R}{2+2r}$

Q. In the circuit shown, if a conducting wire is connected between points A and B, the current in this wire will

1. Flow from A to B
2. Flow in the direction which will be decided by the value of V
3. Be zero
4. Flow form B to A

Q. Find out the value of resistance $R$ in figure.

1. $150\Omega$
2. $500\Omega$
3. $100\Omega$
4. $200\Omega$

Q. A network of resistances is constructed with $R_1$ and $R_2$ as shown in the figure. The potential at the points 1, 2, 3 … n are $V_1,V_2,V_3,\dots V_n$ respectively, each having a potential k times smaller than the previous one.

The ratio $\frac{R_2}{R_3}$ is

1. $\frac{{(k-1)}^2}{k}$
2. $k^2-\frac{1}{k}$
3. $\frac{k}{k-1}$
4. $k-\frac{1}{k^2}$

Q. Find the current flowing through the resistance $R_1$ of the circuit shown in figure, if the resistances are equal to $R_1=10\Omega$, $R_2=10\Omega$ and $R_3=10\Omega$, and the potential of points $1,2$ and $3$ are equal to $V_1=10\text{V}$, $V_2=6\text{V}$ and $V_3=5\text{V}$.

1. $0.1\text{A}$
2. $0.4\text{A}$
3. $0.3\text{A}$
4. $0.2\text{A}$

Q. A wire has resistance $12\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to

1. $12\Omega$
2. $6\Omega$
3. $3\Omega$
4. $24\Omega$

Q. Three resistances of equal value are connected in four different combinations as shown in figure. Arrange them in increasing order of power dissipation

1. $III<II<IV<I$
2. $II<III<IV<I$
3. $I<IV<III<II$
4. $I<III<II<IV$

Q. Find $R_{AB}$ (Call resistances in $\Omega$ )

1. $\frac{8}{3}\Omega$
2. $2\Omega$
3. $9\Omega$
4. $\frac{3}{8}\Omega$

Q. 100 mA current gives a full-scale deflection in a galvanometer of $2\Omega$ . The resistance connected with the galvanometer to convert it into a voltmeter to measure $5V$ is

1. $98\Omega$
2. $52\Omega$
3. $50\Omega$
4. $48\Omega$

Q. Consider 12 resistors arranged symmetrically in shape of a bi - pyramid ABCDEF. Here, ABCD is a square. Point E, point F and center of the square are in the same straight line perpendicular to the plane of the square. The resistance of each resistor is $R$.

The effective resistance between A and C is

1. $\frac{R}{2}$
2. $\frac{R}{3}$
3. $R$
4. None of these

Q. A wire of resistance $0.5\Omega m^{-1}$ is bent into a circle of radius 1 m. An identical wire is connected across a diameter AB as shown in fig. The equivalent resistance is

1. $\pi$ ohm
2. $\pi (\pi +2)$ ohm
3. $\frac{\pi }{(\pi +4)}$ ohm
4. $(\pi +1)$ ohm

Q. When a $12\Omega$ resistor is connected with a moving coil galvanometer, then its deflection reduces from 50 divisions to 10 divisions. The resistance of the galvanometer is

1. $24\Omega$
2. $36\Omega$
3. $48\Omega$
4. $60\Omega$

Q. Find the current flowing through the resistance $R_1$ of the circuit shown in figure, if the resistances are equal to $R_1=10\Omega$, $R_2=10\Omega$ and $R_3=10\Omega$, and the potential of points $1,2$ and $3$ are equal to $V_1=10\text{V}$, $V_2=6\text{V}$ and $V_3=5\text{V}$.

1. $0.1\text{A}$
2. $0.3\text{A}$
3. $0.2\text{A}$
4. $0.4\text{A}$

Q. A copper wire of length 1m and radius 1 mm is joined in series with an iron wire of length 2 m and radius 3 mm and a current is passed through the wires. The ratio of the current density in the copper and iron wires is

1. 2:3
2. 6:1
3. 9:1
4. 18:1

Q. Resistance of each branch in the given figure is $1\Omega$. Equivalent resistance of circuit between point A and B is :

1. $\frac{11}{13}$
2. $\frac{22}{17}$
3. $\frac{7}{9}$
4. $\frac{22}{35}$

Q. A network of resistances is constructed with $R_1$ and $R_2$ as shown in the figure. The potential at the points 1, 2, 3 … n are $V_1,V_2,V_3,\dots V_n$ respectively, each having a potential k times smaller than the previous one.

The current that passes through the resistance $R_2$ nearest to the $V_{\alpha }$ is

1. $\frac{{(k-1)}^2}{k}\frac{V_0}{R_3}$
2. $\frac{{(k+1)}^2}{k}\frac{V_0}{R_3}$
3. $(k+\frac{1}{k^2})\frac{V_0}{R_3}$
4. $\left(\frac{k-1}{k^2}\right)\frac{V_0}{R_3}$

Q. Find $R_{AB}$ All arms have resistance R.

1. $8R$
2. $15R$
3. $\frac{8R}{15}$
4. $\frac{15R}{8}$

Q. A finite square grid, each link having resistance $r=\frac{40}{7}\Omega$, is fitted in a resistance less conducing circular wire. Determine the equivalenet resistance between A and B ( in$\Omega$)

Q. Each branch in the following circuit has a resistance $R$. The equivalent resistance of the circuit between two points $A$ and $B$

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

Q. Given three resistors of $2\Omega ,4\Omega and6\Omega$, the minimum equivalent resistance one can obtain is .

1. 12/11 $\Omega$
2. 11/12 $\Omega$
3. 13/16 $\Omega$
4. 11/12 $\Omega$