Current Electricity · Question 46

A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf's is

1. 3 : 4
2. 3 : 2
3. 5 : 1
4. 5 : 4

The charge flowing through a resistance R varies with time t as Q = at - bt2, where a and b are positive constants. The total heat produced in R is

1. a3R2b
2. a3Rb
3. a3R6b
4. a3R3b

The potential difference (VA - VB) between the points A and B in the given figure is [figure]

1. -3 V
2. +3 V
3. +6 V
4. +9 V

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
2. 46
3. 26
4. 13

Two metal wires of identical dimensions are connected in series. If 1 and 2 are their conductivities, the effective conductivity of the combination is

1. 1 + 2 1 2
2. 1 2 1 + 2
3. 2 1 2 1 + 2
4. 1 + 22 1 2

A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. E0 and a resistance r1. An unknown e.m.f. E is balanced at a length l of the potentiometer wire. The e.m.f. E will be given by

1. E0lL
2. LE0r(r + r1)l
3. LE0rlr1
4. E0r(r + r1) lL

A, B and C are voltmeters of resistance R, 1.5R and 3R respectively as shown in the figure. When some potential difference is applied between X and Y, the voltmeter readings are VA, VB and VC respectively, Then [figure]

1. VA = VB VC
2. VA VB VC
3. VA = VB = VC
4. VA VB = VC

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. drift velocity
2. electric field
3. current density
4. current

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

1. 44
2. 48
3. 32
4. 40

The resistances in the two arms of the meter bridge are 5 and R respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6 l1. The resistance R is [figure]

1. 10
2. 15
3. 20
4. 25