Q. Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is
A) 1 : 4
B) 4 : 1
C) 1 : 2
D) 2 : 1
Explanation
(a) Let the resistance of each heater wire is $R.$ When two wires are connected in series, the heat developed is
$H_{1} = \frac{V^{2}t}{2R}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
When two heater wires are connected in parallel, the heat developed is
$H_{2} = \frac{V^{2}t}{R/2} = \frac{2V^{2}t}{R}\ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
Dividing Eq. (i) by Eq. (ii), we get
$\frac{H_{1}}{H_{2}} = \frac{1}{4}\ or\ \ H_{1}\ :H_{2} = 1\ :4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.