Question

If the current in the wire is doubled then the heat produce will become:
1. Half
2. One fourth
3. Double
4. Four times

Answer 1

Correct Answer - Option 4 : Four times

The correct answer is Four times.

Heating effect of current:

• When the ends of a conductor are connected to a battery, then the free electrons move and the electric current flows through the wire.
• These electrons collide continuously with the positive ions of the wire and thus the energy taken from the battery gets dissipated in the form of heat.
• The effect of electric current due to which heat is produced in a wire when current is passed through it is called the heating effect of current.
• The heat produced in the wire is,

⇒ H ∝ I²

⇒ H ∝ R

⇒ H ∝ t

\(⇒ H=\frac{I^2Rt}{J}\)

Where H = heat, I = current, R = resistance, t = time and J = Joule's equivalent

CALCULATION:

Given I₂ = I₁, R₁ = R₂ = R and t₁ = t₂ = t

• When the current is I₁,

\(⇒ H_{1}=\frac{I_{1}^{2}Rt}{J}\)     -----(1)

• When the current is doubled,

\(⇒ H_{2}=\frac{I_{2}^{2}Rt}{J}\)

\(⇒ H_{2}=\frac{(2I_{1})^{2}Rt}{J}\)

\(⇒ H_{2}=\frac{4I_{1}^{2}Rt}{J}\)     -----(2)

By equation 1 and equation 2,

⇒ H₂ = 4H