Null point with 1V cell comes out to be 55cm and with R = 10Ω it is 50 cm. What is the internal resistance of the cell?

0.5Ω
0.4Ω
1Ω
0.2Ω

Solution

Current I₁ in the following circuit is

0.4 A
– 0.4 A
0.8 A
–0.8 A

Solution

Two resistances R₁ and R₂ are made of different materials.The temperature coefficient of the material of R₁ is α and that of material of R₂ is– β. The resistance of the series combination of R₁ and R₂ will not change with temperature if ^R₁⁄_R₂ equal to

^α⁄_β
\(\frac{\alpha +\beta }{\alpha -\beta }\)
\(\frac{\alpha^{2} +\beta^{2} }{2 \alpha \beta }\)
^β⁄_α

Solution

The length of a given cylindrical wire is increased by 100%.Due to the consequent decrease in diameter the change in the resistance of the wire will be

100%
50%
300%
200%

Solution

A 4 m long wire of resistance 8Ω is connected in series with a battery of e.m.f. 2 V and a resistor of 7 Ω. The internal resistance of the battery is 1 Ω. What is the potential gradient a long the wire?

1.00 V m^–1
0.75 V m^–1
0.50 Vm^–1
0.25 V m^–1

Solution

A wire has a resistance 12 Ω. It is bent in the form of acircle.The effective resistance between two points on any diameter is

6 Ω
3 Ω
12 Ω
24 Ω

Solution

Resistance of the wire of a semicircle = 12/2 =6For equivalent resistance between two points on any diameter, 6Ω and 6Ω are in parallel.

or

If a wire of resistance R is bent in the form of a circle,the effective resistance between the ends of a diameter= R/4.

The belt of an electrostatic generator is 50 cm wide and travels at 30 cm/sec. The belt carries charge into the sphere at a rate corresponding to 10^–4 ampere. What is the surface density of charge on the belt.

6.7 × 10^-5Cm^-2/s
6.7 × 10^-4Cm^-2/s
6.7 × 10^-7Cm^-2/s
6.7 × 10^-8Cm^-2/s

Solution

J = I/A = 10^-4/(0.300.50).

= 6.7 × 10^-4 Cm^-2/s= 6.7 × 10^-4 Am^-2

In the network shown below, the ring has zero resistance.The equivalent resistance between the point A and B is

Solution

All the edges of a block with parallel faces are unequal. Its longest edge is twice its shortest edge. The ratio of the maximum to minimum resistance between parallel faces is

2
4
8
indeterminate unless the length of the third edge is specified

Solution

A non-conducting ring of radius R has charge Q distributed unevenly over it. If it rotates with an angular velocity ω, the equivalent current will be

zero
Qω
\(Q\frac{\omega }{2\pi }\)
\(Q\frac{\omega }{2\pi R}\)

Solution

With each rotation, charge Q crosses any fixed point P near the ring.Number of rotations per second= ω/2π.

∴ charge crossing P per second= current =\(\frac{Q\omega }{2\pi }\)

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