Electricity

AN electrical instrument used to control a current by varying the resistance is known as______

• Resistor

• Coulometer

• Plug key

• Rheostat

• Variable resistance

Voltmeter is also known as ________

A set of 'n' identical resistors each of resistance RΩ, when connected in series have an effective resistance XΩ and when connected in parallel each resistor is of RΩ and their effective resistance is is YΩ. Find the product of XΩ and YΩ.

• R

• 2R

• R²

• √R

In an electron beam A total of of 6 x 10¹⁶ electrons flow through any perpendicular cross-section per second. Calculate the current in the beam.

• 9.5 x 10^-3

• 9.6 x 10^-6

• 9.6 mA

• 9.6 A

Answer explanation

Given:

Time taken=1 second, No. of electrons=6 x 10¹⁶

Find: The current flowing through the beam

Solution:

We know that I=Q∕T, -1

Also, Q= n x e where 'e' is the charge of one electron -2

From 1 and 2 we could write:

I=ne/T

I=6 x 10¹⁶ x (1.6 x 10^-19 )/1

I= 9.6 x 10^-3 A

Hence Current flowing through the beam=9.6 x 10^-3 or 9.6 mA

AN electron bas an aperture of 1.0mm² . A total of of 6 x 10¹⁶ electrons flow through any perpendicular cross section per second. Calculate the current density in this case.

• 9.6 x 10^-3 A/m²

• 9.6 x 10^-3 A

• 9 x 10⁵ Am^-2

• None of the above

Answer explanation

Given:

Area of the aperture=1 mm²,

No. of electrons=6 x 10¹⁶

Find: The current density

Solution:

We know that Current flowing through the beam=9.6 x 10^-3

Also, Current density(J)= I/A where A is Area

→ J= 9.6 x 10^-3 / 1mm²

We know that, 1mm= 10^-3

So, 1mm² = (10^-3 )²

→J=9.6 x 10^-3 / 10^-6

Hence, Current density= 9.6 x 10³ Am^-2

How many electron is present in one coulomb of charge?

• 6.23 x 10¹⁸

• 1.6 x 10^-19

• 6.25 x 10¹⁸

• 1.6 x 10¹⁸

What is the maximum resistance which can be made using five resistors each of 1/5 Ω?

• 5 Ω

• 10 Ω

• 1/5 Ω

• 1 Ω

Answer explanation

If we need to calculate the maximum resistance, we must connect the resistors in series.

Total resistance= R₁ + R₂ + R₃ ... R_n or in case of identical resistors: R_t = n x R where r is no. of resistors

R= 1/5 x 5

= 1

= 1Ω

Hence, the maximum resistance that can be created by given resistors is 1Ω

Maximum resistance can be obtained in which of the following cases?

• Parallel

• Semi-parallel

• Semi-series

• Series

A piece of wire of resistance R is cut into five equal parts. These parts are then arranged in parallel. If the equivalent resistance of this combination is R′, then the ratio R/R′ is _____.

• 5

• 25

• 1/5

• 1/25

Answer explanation

Given: Equivalent resistance is R',

Find: Ratio R/R'

Solution: When resistors are identical and in a parallel arrangement, total resistance= R/n where n is the no. of resistors and R is the resistance of each resistor

Total resistance= (R/5)/5

R'= R/25

R'/R= 25

Hence, Ratio required= 25

What is the minimum resistance which can be made using five resistors each of 1/5 Ω?

• 1/25Ω

• 1/5Ω

• 1/10Ω

• 25Ω

Answer explanation

If we are supposed to find the minimum resistance, we must connect the resistors in parallel.

So, R_t = R/n when resistors are identical

∴ Total resistance= (1/25)/ 5

Hence, Minimum resistance= 1/25