Resistivity Formula MCQs with Solutions

Ans. (d) Length

Explanation: The resistance of a wire is directly proportional to its length. In other words, the resistance of a wire increases with the increase in length. The resistance of a wire is also inversely proportional to its cross-sectional area.

Ans. a) Current via each resistance is the same

Explanation: In a series combination, the current across the circuit components always remains constant. However, in a parallel combination, the voltage found across the circuit components is constant.

Ans. b) R/(n-1)

Explanation: As per what is given,

R_g = R 

I = nI_g

The shunt resistance which is required, R_s = \(\frac{I_gR_g}{I - I_g}\)

⇒ R_s = \(\frac{I_gR}{nI_g - I_g} = \frac{R}{n-1}\)

Ans. a) 100 Ω

Explanation: Since we are aware that,

I = \(\frac{V}{R} \)

We can also say that, \( \frac{I_1}{I_2} = \frac{R_1}{R_2}\)

R₁ = 900 Ω

Thus, the flow of current via 900 Ω resistance minimized by 90%

The current ratio = 10% : 90% = 1:9

\(\therefore \ \frac{1}{9} = \frac{R_2}{R_1}\)

= \(\frac{1}{9} = \frac{R_2}{900}\)

= \(R_2 = \frac{900}{9} = 100\)

Hence, Shunt = 100 Ω.

Ans. b) End Correction

Explanation: It is assumed, in a meter bridge experiment, that resistance of the given L-shaped plate is supposed to be negligible, but actually it isn’t. The error that is is given rise to due to this is known as end error. In order to remove this, the resistance box and the unknown resistance will have to be interchanged, with further mean reading.

Ans. a) R = r

Explanation: With the given data, the maximum current which is drawn from the cell will be the case if only the external resistance is minimum.
The current in the circuit can be expressed by:

I = \(\frac{E}{R+r}\)

Therefore, the smallest value of the given denominator will offer maximum current. For maximum current, the value of R must be equivalent to zero.

Ans. (a) 0.0039

Explanation: The temperature coefficient of resistivity of silver can be expressed as 0.0039.

Ans. c) Superconductivity

Explanation: The resistivity of a few metals or alloys declines to zero when they are chilled below a certain temperature. This phenomenon is usually called Superconductivity.

Ans. a) \(\Omega - cm\)

Explanation: After rearranging the equation of R = \(\rho \frac{l}{A}\)

We get, \(\rho = R \frac{A}{l}\)

Upon substituting the CGS units, we can obtain:

ρ = \(\Omega \frac{cm^2}{cm}\) 

Thus, \(\Omega - cm\)

Ans. a) Nature of the Material

Explanation: Electrical resistivity, in general, does not depend on the geometrical property of any material. Some properties that it does not depend upon are its length, thickness, shape and more. Thus, it only depends on what the nature of the material is.

Ans. c) 7.5 \(\Omega m\) 

Explanation: According to the question,

• R = 3 Ω
• l = 0.2 m and
• A = 0.5 m²

Hence, the Resistivity formula: \(\rho = \frac{RA}{l}\)

After value substitution, we get:

 \(\rho = \frac{3 \times 0.5}{0.2} = 7.5 \Omega m\)