Question

A heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

• A. 2 : 1
• B. 1 : 2
• C. 1 : 4
• D. 4 : 1

Answer 1

Answer: (A)

2 : 1

Answer 2

If suppose resistance of the coil is R so resistance of it’s half will be $\frac{R}{2}$. Hence by using $H = \frac{V^{2}t}{R} \Rightarrow H \propto \frac{1}{R}$

⇒ $\frac{H_{Half}}{H_{Full}} = \frac{R_{Full}}{R_{Half}} = \frac{R}{R/2} = \frac{2}{1}$

Note: In general if coil is divided in n equal parts then heat produced by each part will be n times of the heat produced by coil it self i.e. H′ = Nh