Series and Parallel Combination of Resistors

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. A ring is made of a wire having a resistance $R_0=12\Omega$. Find the points $A$ and $B$ as shown in the figure, at which a current carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3}\Omega$.

1. $\frac{l_1}{l_2}=\frac{8}{5}$
2. $\frac{l_1}{l_2}=\frac{1}{3}$
3. $\frac{l_1}{l_2}=\frac{1}{2}$
4. $\frac{l_1}{l_2}=\frac{5}{8}$

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

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. A coil has resistance $30\text{ohm}$ and inductive reactance $\text{20 Ohm}$ at $\text{50 Hz}$ frequency. If an ac source, of $\text{200 volt, 100 Hz}$, is connected across the coil, the current in the coil will be :

1. $\text{4.0 A}$
2. $\text{8.0 A}$
3. $\frac{20}{\sqrt{13}}\text{A}$
4. $\text{2.0 A}$

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

1. 2 V
2. 2/3 V
3. 8/9 V
4. 4/3 V

Q. Potentiometer wire $\text{PQ}$ of $1\text{m}$ length is connected to a standard cell $E_1$. Another cell $E_2$ of emf $1.02\text{V}$ is connected with a resistance $r$ and a switch $S$ as shown in circuit diagram. With switch $S$ open, null position is obtained at a distance of $51\text{cm}$ from $\text{P}$. Calculate the e.m.f. of cell $E_1$.

1. $2.2\text{V}$
2. $2\text{V}$
3. $1.8\text{V}$
4. $1.02\text{V}$

Q. A galvanometer of $50$ ohm resistance has $25$ divisions. A current of $4\times {10}^{-4}\text{A}$ gives a deflection of one division. To convert this galvanometer into a voltmeter having a range of $25$ $\text{V}$, it should be connected with a resistance of

​​​​​​​$[$1 Mark$]$

1. $245\Omega$ in parallel
2. $2550\Omega$ in series
3. $2450\Omega$ in series
4. $2500\Omega$ in parallel

Q. In the circuit shown below, the current in the $1\Omega$ resistor is

1. $1.3\text{A}$, from $\text{P}$ to $\text{Q}$
2. $0\text{A}$
3. $0.13\text{A}$, from $\text{Q}$ to $\text{P}$
4. $0.13\text{A}$, from $\text{P}$ to $\text{Q}$

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

1. 
2. 4 ohm
3. 
4. 8 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. A ring is made of a wire having a resistance $R_0=12\Omega$. Find the points $A$ and $B$ as shown in the figure, at which a current carrying conductor should be connected so that the resistance $R$ of the sub-circuit between these points is equal to $\frac{8}{3}\Omega$.

1. $\frac{l_1}{l_2}=\frac{8}{5}$
2. $\frac{l_1}{l_2}=\frac{1}{3}$
3. $\frac{l_1}{l_2}=\frac{5}{8}$
4. $\frac{l_1}{l_2}=\frac{1}{2}$

Q. $\text{Statement-}1:$ Conductivity of a metallic conductor decreases with increase in temperature.
$\text{Statement-}2:$ On increasing temperature the number of free electrons in the metallic conductor decreases.

1. $\text{Statement-}1$ is true, $\text{Statement-}2$ is true; $\text{Statement-}2$ is a correct explanation for $\text{Statement-}1$
2. $\text{Statement-}1$ is true, $\text{Statement-}2$ is true; $\text{Statement-}2$ is NOT a correct explanation for $\text{Statement-}1$
3. $\text{Statement-}1$ is true, $\text{Statement-}2$ is false
4. $\text{Statement-}1$ is false, $\text{Statement-}2$ is true

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

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

Q. A Zener of power rating $1W$ is to be used as a voltage regulator. If zener has a breakdown of $5V$ and it has to regulate voltage which fluctuated between $3V$ and $7V$, what should be the value of $R_s$ for safe operation (Fig.)?

Q.

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

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

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

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

Q. The equivalent resistance between points $A$ and $B$ is

1. $32.5\Omega$
2. $22.5\Omega$
3. $2.5\Omega$
4. $42.5\Omega$

Q. Two metal cubes with $3\text{cm}$ edges of copper and aluminium are arranged as shown in the figure. The total thermal current from one reservoir to the other will be
$(\text{Thermal conductivity,}{K}_{Cu}=385\text{W/m-K},K_{Al}=209\text{W/m-K})$

1. $1426\text{W}$
2. $1526\text{W}$
3. $1626\text{W}$
4. $1726\text{W}$

Q. If $L,R,C$ denote inductance, resistance, and capacitance, respectively. Then dimension of$\frac{L}{R^{2}C}$ are

1. $\left[M^0{L}^{0}T\right]$
2. $\left[M^0{L}^0{T}^0\right]$
3. $\left[A^{-1}{M}^0{L}^0{T}^{-1}\right]$
4. $\left[ML{T}^{-1}\right]$

Q.

In a Wheatstone bridge (see fig.), resistances P and Q are approximately equal. When $R=400\Omega$, the bridge is equal. When $R=400\Omega$, the bridge is balanced. On inter-changing P and Q, the value of R, for balance, is $405\Omega$. The value of X is close to

1. $403.5ohm$

2. $404.5ohm$

3. $401.5ohm$

4. $402.5ohm$

Q. three amplifier each having voltage gain 100 are connected in series and parallel seprately find resul†an t gain in series and parallel respectively ?

Q. If $X,Y$ and $Z$ in figure are identical lamps, which of the following changes to the brightness of the lamps occur when switch $S$ is closed?

1. $X$ stays the same, $Y$ decreases
2. $X$ increases, $Y$ stays the same
3. $X$ increases, $Y$ decreases
4. $X$ decreases, $Y$ increases

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

Q. A meterbridge setup (as shown) is used to determine end correction at $\text{A}$ and $\text{B}$. When a resistance of $15\Omega$ is used in left gap and of $20\Omega$ in right gap then null point is $42\text{cm}$ from $\text{A}$, now if these resistances are intercharged null point is $57\text{cm}$ from $\text{A}$ then end correction at $\text{A}$ & $\text{B}$ are

1. $3\text{cm},2\text{cm}$
2. $6\text{cm},1\text{cm}$
3. $1.5\text{cm},1.5\text{cm}$
4. $1\text{cm},2\text{cm}$

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

Q. A battery of internal resistance $4$ $ohm$ is connected to the network of resistance as shown. In order that the maximum power can be delivered to the network, the value of $R$ in ohm should be

1. $18$
2. $2$
3. $\frac{8}{3}$
4. $\frac{4}{9}$

Q.

A voltmeter of resistance 400 $\Omega$ is used to measure the potential difference across the 100 $\Omega$ resistor in the circuit shown in figure (32-E24). (a) What will be the reading of the voltmeter? (b) What was the potential difference across 100 $Omega$ before the voltmeter was connected ?

Q.

Is the superposition theorem applicable to AC circuits?