Question

If a wire in the circuit is replaced with a wire of resistivity four times and the length and cross-sectional area is the same. Then the current in the circuit will become:
1. One fourth
2. Four times
3. Half
4. Double

Answer 1

Correct Answer - Option 1 : One fourth

CONCEPT:

Resistance:

• The property of any conductor that opposes the flow of electric current through it and depends on the shape and size of the materials, temperature, and nature of the materials is called resistance.
  • It is denoted by R and the SI unit is the ohm (Ω).
• The resistance is given by:

​\(⇒ R=\frac{ρ l}{A}\)

Where ρ = specific resistance, l = length of the wire, and A = cross-sectional area of the wire

Ohm's law

• Ohm’s law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperature remain constant.

​⇒ V = IR

Where V = voltage, I = current and R = resistance

CALCULATION:

Given l₁ = l₂ = l, A₁ = A₂ = A and ρ₂ = 4ρ₁

For case 1, (ρ₁ = ρ)

\(⇒ R_{1}=\frac{ρ l}{A}\)     -----(1)

The current in the circuit,

\(\Rightarrow I_{1} = \frac{V}{R_{1}}\)

\(\Rightarrow I_{1} = \frac{VA}{\rho l}\)     -----(2)

For case 2, (ρ2 = 4ρ)

\(⇒ R_{2}=\frac{4ρ l}{A}\)     -----(3)

The current in the circuit,

\(\Rightarrow I_{2} = \frac{V}{R_{2}}\)

\(\Rightarrow I_{2} = \frac{VA}{4\rho l}\)     -----(4)

By equation 2 and equation 4,

\(\Rightarrow I_{2} = \frac{I_{1}}{4}\)

• Hence, option 1 is correct.