Series Combination of Cells

Q. If potential (in $\text{(in Volt)}$ in a region is expressed as,
$V(x,y,z)=6xy-y+2yz$
The electric field $\text{(in N/C)}$ at point $(1,1,0)$ is

1. $-(6\hat{i}+9\hat{j}+\hat{k})$
2. $-(3\hat{i}+5\hat{j}+3\hat{k})$
3. $-(6\hat{i}+5\hat{j}+2\hat{k})$
4. $-(2\hat{i}+3\hat{j}+\hat{k})$

Q.

In a potentiometer experiment, the balancing with a cell is at a length of $240cm$. On shunting the cell with a resistance of $2\Omega$, the balancing length becomes $120cm$. The internal resistance of the cell is

1. $1\Omega$

2. $0.5\Omega$

3. $4\Omega$

4. $2\Omega$

Q. In the arrangement shown in given figure current from $A$ to $B$ is increasing in magnitude. Induced current in the loop will

1. have clockwise direction
2. have anticlockwise direction
3. be zero
4. oscillate between clockwise and anticlockwise

Q. Determine the charge on the capacitor in the following circuit

1. $110\mu C$
   
2. $60\mu C$
   
3. $200\mu C$
   
4. $2\mu C$
   

Q.

Given potential difference, $V=(8\pm 0.5)V$ and current, $I=(2\pm 0.2)A$. The value of resistance $R$ in $\Omega$ is

1. $4\pm 8\%$
2. $4\pm 10\%$
3. $4\pm 16.25\%$
4. $4\pm 6.25\%$

Q. The resistance of an ammeter is $13\Omega$ and its scale is made for a current upto 100 amp. After an additional shunt has been connected to this ammeter it becomes possible to measure current upto 750 amp.. The value of shunt resisance is

1. $2\Omega$
2. $0.2\Omega$
3. $20\Omega$
4. $200\Omega$

Q. The electric potential in a certain region is expressed by v = 6x-8xy${}^2$-8y+6yz-4z${}^2$ volts. The magnitude of the force acting on a charge of 2 C situated at the origin will be

1. 2 N
2. 6 N
3. 8 N
4. 20 N

Q. In the circuit shown below the cells $E_1$ and $E_2$ have emf’s 4 V and 8 V and internal resistance 0.5 ohm and 1 ohm respectively. Then the potential difference across cell $E_1$ and $E_2$ will be

1. 3.75 V, 7.5 V
2. 4.25 V, 7.5 V
3. 3.75 V, 3.5 V
4. 4.25 V, 4.25 V

Q. Two batteries A and B each of emf 2 volt are connected in series to external resistance $R=1\Omega$. Internal resistance of A and B are $1.9\Omega$ and $0.9\Omega$ respectively. What is the potential difference between the terminals of battery A ?

1. 2 V
2. 3.8 V
3. 0
4. None of these

Q. Two inductors $L_1$(inductance $1mH$, internal resistance $3\Omega$) and $L_2$(inductance $2mH$, internal resistance $4\Omega$), and a resistor R (resistance $12\Omega$) are all connected in parallel across a $5V$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current ($I_{max}/I_{min}$) drawn from the battery is

Q. In the following circuit the potential difference between P and Q is

1. 15 V
2. 10 V
3. 5 V
4. 2.5 V

Q. In the given circuit diagram, when the current reaches steady state in the circuit, the charge on the capacitor of capacitance $C$ will be

1. $CE\frac{r_1}{(r_1+r)}$
2. $CE$
3. $CE\frac{r_1}{(r_2+r)}$
4. $CE\frac{r_2}{(r+r_2)}$

Q. A galvanometer can be converted to a voltmeter of full-scale deflection $V_0$ by connecting a series resistance $R_1$ and can be converted to an ammeter of full -scale deflection $I_0$ by connecting a shunt resistance $R_2$. What is the current flowing through the galvanometer at its full-scale deflection?

1. $\frac{V_0-I_0{R}_2}{R_1-R_2}$
2. $\frac{V_0+I_0{R}_2}{R_1+R_2}$
3. $\frac{V_0-I_0{R}_1}{R_1-R_2}$
4. $\frac{V_0+I_0{R}_1}{R_1+R_2}$

Q.

Why DC current is not used in homes?

Q.

Please explain the concept of short circuit

Q.

How do you verify superposition theorem?

Q. A battery of emf 12 V and internal resistance $2\Omega$ is connected to a $4\Omega$ resistor as shown in the figure.
(a) Show that a voltmeter when placed across the cell and across the resistor, in turn, gives the same reading.
(b) To record the voltage and the current in the circuit, why is the voltmeter placed in parallel and the ammeter in series in the circuit ?

Q. In the given branch $AB$ of a circuit, a current, $I=(10t+5)\text{A}$ is flowing, where $t$ is time in second. At $t=0$, the potential difference between points $A$ and $B$, $V_A-V_B$ is -

1. $15\text{V}$
2. $-5\text{V}$
3. $-15\text{V}$
4. $5\text{V}$

Q. 71. A 100 microfarad capacitor is connected across 220 V, 50 hz power supply. What is the displacement current throughthe capacitor? 1)3 A 2)5 A 3)7 A 4)9 A

Q.

The current in 2 ohm resistor shown in the figure below is

1. 0.4A

2. 1 A

3. 1.2 A

4. 1.4 A

Q. In a mixed grouping of identical cells 5 rows are connected in parallel and each row contains 10 cells. This combination send a current i through an external resistance of $20\Omega$. If the emf and internal resistance of each cell is 1.5 volt and $1\Omega$ respectively then the value of i is

1. 0.14 A
2. 0.25 A
3. 0.75 A
4. 0.68 A

Q.

The energy dissipated by a resistor is $10mJ$ in $1s$ when an electric current of $2mA$ flows through it. The resistance is ________. (Round off to the nearest Integer)

Q. A group of N cells whose emf varies directly with the internal resistance as per the equation $E_n$= 1.5 $r_N$are connected as shown in the figure below. The current I in the circuit is

1. 0.51 amp
2. 0.15 amp
3. 1.5 amp
4. 5.1 amp

Q. The resistance of an electrolyte varies with temperature $T$ as $R_T=\frac{R_0}{1+\alpha T^{\prime }}$, where $R_0$ and $\alpha$ are constants. $A$ constant potential difference $V$ is applied to the two electrodes (each of surface area $A$) which are dipped in this electrolyte. If $T_0$ is the temperature of the surroundings, the loss of heat to the surroundings per unit surface area per unit time is governed by the same relation $H=k(T-T_0)A,$ the steady state temperature is

1. none of these
2. $\frac{V^2}{RkA}$
3. $\frac{(V^2+kA{R}_{0}T)}{(k{R}_{0}A-\alpha V^2)}$
4. $\frac{V^2}{k{R}_{0}A-\alpha V^2}$

Q.

Consider the circuit shown below where all resistors are of 1 k $\Omega$

If a current of magnitude 1 mA flows through the resistor marked X, what is the potential difference measured between point P and Q?

1. 21V

2. 68V

3. 55V

4. 34V

Q. Consider an arrangement of six large parallel plates as shown in the figure, each of the plate’s area $A$. Initially when battery was not connected all plates were uncharged. The emf of the battery is $V$. Choose the correct option(s) after connecting the battery (in steady state):

1. Total work done by battery is $\frac{{\epsilon }_{0}A}{d}{V}^2$
2. Electric field between plates 3 and 4 is $\frac{V}{2d}$
3. Potential difference between plate 2 and 5 is $\frac{V}{2}$
4. Potential difference between plate 1 and 5 is $\frac{V}{2}$

Q. A parallel combination of an $8\Omega$resistor and an unknown resistor R is connected in series with a $16\Omega$resistor and a battery. This circuit is then disassembled and the three resistors are connected in series with each other and the same battery. If in both arrangements, the current through the $8\Omega$resistor is the same, then R is (Take $\sqrt{2}=1.41$) and write upto two digits after the decimal point.)

Q.

In purely inductive circuits, the current:

1. 

2. 

3. is in phase with the voltage

4. none of the above

Q. Two cells of same emf are in series with an external resistance R. The internal resistance $r_1$ > $r_2$. The p.d across the $1^{st}$ cell is found to be zero the value of R is

1. $r_1+r_2$
   
2. $r_1-r_2$
   
3. $\frac{r_1+r_2}{2}$
   
4. $\frac{r_1-r_2}{2}$

Q. Resistors $P,Q$ and $R$ in the circuit have equal resistances. If the battery is supplying a total power of $12\text{W}$, what is the power dissipated as heat in resistor $R$ ?

1. $2\text{W}$
2. $6\text{W}$
3. $3\text{W}$
4. $8\text{W}$