Series and Parallel Combination of Resistors

Q. Five equal resistances each of resistance R are connected as shown in the figure. A battery of 4 volts is connected between A and B. The current flowing in AFCEB will be

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

Q. The current I in the circuit shown in figure is

1. $\frac{1}{45}$ A
2. $\frac{1}{15}$ A
3. $\frac{1}{10}$ A
4. $\frac{1}{5}$ A

Q. For the network shown in the figure, the value of the current $i$ is

1. $\frac{5V}{9}$
2. $\frac{18V}{5}$
3. $\frac{9V}{35}$
4. $\frac{5V}{18}$

Q. What is the equivalent resistance of the network shown in figure? The numbers indicate resistance in ohms

1. $8$ ohm
2. $\frac{16}{3}$ ohm
3. $4$ ohm
4. $\frac{16}{5}$ ohm

Q. Find the equivalent resistance between points A and B of the following network shown in the given diagram?

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

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

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

Q. Heat flows through a composite slab, across a temperature difference $\Delta T$ as shown below. The depth of the slab is $1\text{m}$. The conductivity ($K$) values are in $\text{W/mK}$. The overall thermal resistance in $\text{K/W}$ is
(rounded to the nearest integer)

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

Q. Seven resistances are connected as shown in figure. The equivalent resistance between A and B is

1. $3\Omega$
2. $4\Omega$
3. $4.5\Omega$
4. $5\Omega$

Q. Two resistors of resistance $R_1$and $R_2$having $R_1>R_2$ are connected in parallel. For equivalent resistance R, the correct statement is

1. $R>R_1+R_2$
2. $R_1<R<R_2$
3. $R_2<R<(R_1+R_2)$
4. $R<R_1$

Q. The rms value of an alternating current, which when passed through a resistor produces heat three times of that produced by a direct current of 2 A in the same resistor, is (1) 6 A (2) 3 A (3) 2 A (4) 2 root3 A

Q. In the diagram, resistance between any two junctions is R. Equivalent resistance across terminals A and B is

1. $\frac{11R}{7}$
2. $\frac{18R}{11}$
3. $\frac{7R}{11}$
4. $\frac{11R}{18}$

Q. The current i in the circuit will be

1. $\frac{1}{45}$ ampere
2. $\frac{1}{15}$ ampere
3. $\frac{1}{10}$ ampere
4. $\frac{1}{5}$ ampere

Q. In a meter bridge, the balancing length from left is found to be $20cm$ when standard resistance of $1\Omega$ is in right gap. The value of unknown resistance is

1. $0.25\Omega$
2. $0.4\Omega$
3. $0.5\Omega$
4. $4\Omega$

Q. In the circuit, the potential difference across PQ will be nearest to

1. 9.6 V
2. 6.6 V
3. 4.8 V
4. 3.2 V

Q. If a cell of internal resistance $1.5\Omega$ and emf of $1.5V$ balances $500cm$ on a potentiometer wire, now by what length would the balance point shift if a cell of internal resistance $2\Omega$ and emf of $2V$ is connected in parallel (along the same polarity) with the prior cell?

1. $71.4cm$ towards left
2. $71.4cm$ towards right
3. $125cm$ towards right
4. Does not shift

Q. A cell of emf $\epsilon$ & and internal resistance r is connected across circuit as given in figure. For what value of R heat generated in outer circuit is maximum, $\epsilon =10V$ & $r=\frac{10}{3}\Omega$

1. $R=5\Omega$
2. $R=3\Omega$
3. $R=10\Omega$
4. Heat generated is independent of R

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

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

Q. Given three resistors of $2\Omega ,4\Omega and6\Omega$, what will be the minimum equivalent resistance one can obtain through their various arrangements?

1. $\frac{12}{11}\Omega$
2. $\frac{11}{12}\Omega$
3. $\frac{13}{16}\Omega$
4. $1\Omega$

Q. The resistance per unit length of a wire is ${10}^{-6}\Omega /m$. It is bent in the form of a circle of diameter 2 m. A wire of same material and cross sectional area is connected across its diameter. The total resistance across its diameter $AB$ will be

1. $\frac{4}{3}\pi \times {10}^{-6}\Omega$
2. $\frac{2}{3}\pi \times {10}^{-6}\Omega$
3. $0.88\times {10}^{-6}\Omega$
4. $14\times {10}^{-6}\Omega$

Q. A wire has linear resistance $\rho$ (in $\Omega /m$). Find the resistance $R$ between points $A$ and $B$ if the side of the larger square is ${}^{\prime }{d}^{\prime }$.

1. $\rho d/\sqrt{2}$
2. $\sqrt{2}\rho d$
3. $2\rho d$
4. None of these

Q. A galvanometer of resistance $20\Omega$ is to be converted into an ammeter of range $1A$. If a current of $1mA$ produces full-scale deflection, the shunt required for the purpose is

1. $0.01\Omega$
2. $0.05\Omega$
3. $0.02\Omega$
4. $0.04\Omega$

Q. A uniform wire of resistance 4 ohm is bent into the form of a circle of radius r. A specimen of the same wire is connected along the diameter of the circle. What is the equivalent resistance across the ends of this wire?

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

Q. A galvanometer of resistance $20\Omega$ is to be converted into an ammeter of range $1A$. If a current of $1mA$ produces full-scale deflection, the shunt required for the purpose is

1. $0.01\Omega$
2. $0.05\Omega$
3. $0.02\Omega$
4. $0.04\Omega$

Q.

Twelve identical resistance are arranged to form a cubical structure find the effective resistance between .
1 and 8

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

Q. Calculate equivalent resistance between $X$ and $Y$. Each resistance is $1\Omega$.

1. $\frac{11}{18}\Omega$
2. $\frac{7}{8}\Omega$
3. $2\Omega$
4. $4\Omega$

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