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A potentiometer circuit is set up as shown. The potential gradient across the potentiometer wire is k volt/cm and the ammeter, present in the circuit, reads 1.0 A when the two-way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1 and 3, is plugged in, are found to be at lengths ${l}_{1}cm$ and ${l}_{2}cm$ respectively. The magnitudes, of the resistors R and X, in ohm, are then, equal, respectively, to

1. $k({l}_{2}-{l}_{1})andk{l}_{2}$

2. $k{l}_{1}andk({l}_{2}-{l}_{1})$

3. $k({l}_{2}-{l}_{1})andk{l}_{1}$

4. $k{l}_{1}andk{l}_{2}$

The resistance in the two arms of the balanced meter bridge as shown in figure are 5 and R, respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6l_{1}. The resistance 'R' is :

1. 10

2. 15

3. 20

4. 25

Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance.

The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be:

1. 2: 1

2. 4: 9

3. 9: 4

4. 1: 2

See the electrical circuit shown in this figure. Which of the following equations is a correct equation for it?

1. ${\epsilon}_{1}-({i}_{1}+{i}_{2})R-{i}_{1}{r}_{1}=0$

2. ${\epsilon}_{2}-{i}_{2}{r}_{2}-{\epsilon}_{1}-{i}_{1}{r}_{1}=0$

3. $-{\epsilon}_{2}-({i}_{1}+{i}_{2})R+{i}_{2}{r}_{2}=0$

4. ${\epsilon}_{1}-({i}_{1}+{i}_{2})R+{i}_{1}{r}_{1}=0$

1. ${\epsilon}_{1}-({i}_{1}+{i}_{2})R-{i}_{1}{r}_{1}=0$

2. ${\epsilon}_{2}-{i}_{2}{r}_{2}-{\epsilon}_{1}-{i}_{1}{r}_{1}=0$

3. $-{\epsilon}_{2}-({i}_{1}+{i}_{2})R+{i}_{2}{r}_{2}=0$

4. ${\epsilon}_{1}-({i}_{1}+{i}_{2})R+{i}_{1}{r}_{1}=0$

A wire of resistance 4Ω is stretched to twice its original length. The resistance of stretched wire would be :

1. 4Ω

2. 8Ω

3. 16Ω

4. 2Ω

1. 4Ω

2. 8Ω

3. 16Ω

4. 2Ω

A filament bulb (500 W, 100 V) is to be used in a 230 V main supply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is :

1. 230 $\mathrm{\Omega}$

2. 46 $\mathrm{\Omega}$

3. 26 $\mathrm{\Omega}$

4. 13 $\mathrm{\Omega}$

A potentiometer wire has length 4 m and resistance 8$\Omega $. The resistance that must be connected in series with the wire and an accumulator of emf 2V, so as to get a potential gradient 1 mV per cm on the wire is

1. 32 $\Omega $

2. 40 $\Omega $

3. 44 $\Omega $

4. 48 $\Omega $

1. 32 $\Omega $

2. 40 $\Omega $

3. 44 $\Omega $

4. 48 $\Omega $

In the circuit shown, if a conducting wire is connected between points *A* and *B*, the current in this wire will: (All resistance given in ohms)

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 from B to A

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 from B to A

Across a metallic conductor of non-uniform cross-section, a constant potential difference is applied. The quantity which remains constant along the conductor is :

1. current density

2. current

3. drift velocity

4. electric field

1. current density

2. current

3. drift velocity

4. electric field

A carbon resistor of (47 ± 4.7) kΩ is to be marked with rings of different colours for its identification. The colour code sequence will be:

1. Violet - Yellow - Orange - Silver

2. Yellow - Violet - Orange - Silver

3. Yellow - Green - Violet - Gold

4. Green - Orange - Violet - Gold

The charge following through a resistance R varies with time t as Q = at-bt^{2}, where a and b are positive constants. The total heat produced in R is:

1. $\frac{{a}^{3}R}{3b}$

2. $\frac{{a}^{3}R}{2b}$

3. $\frac{{a}^{3}R}{b}$

4. $\frac{{a}^{3}R}{6b}$

1. $\frac{{a}^{3}R}{3b}$

2. $\frac{{a}^{3}R}{2b}$

3. $\frac{{a}^{3}R}{b}$

4. $\frac{{a}^{3}R}{6b}$

A student measures the terminal potential difference (V) of a cell (of emf $\epsilon $ and internal resistance r) as a function of the current (I) flowing through it. The slope and intercept of the graph between V and I, respectively, equal to :

1. E and -r

2. -r and E

3. r and -E

4. -E and r

1. E and -r

2. -r and E

3. r and -E

4. -E and r

In the given circuit, with a steady current, the potential drop across the capacitor must be :

(1) *V*

(2) *V / *2

(3) *V */ 3

(4) 2*V */ 3

In the circuit shown in the figure, the current through** :**

(1) The 3Ω resistor is 0.50*A*

(2) The 3Ω resistor is 0.25 *A *

(3) The 4Ω resistor is 0.50*A*

(4) The 4Ω resistor is 0.25 *A *

As the switch S is closed in the circuit shown in the figure, the current passed through it is:

(1) 4.5 A

(2) 6.0 A

(3) 3.0 A

(4) Zero

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