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Question: Two heater wires of equal length are first connected in series and then in parallel. The ratio of he...

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

2 : 1

B

1 : 2

C

4 : 1

D

1 : 4

Answer

1 : 4

Explanation

Solution

Both the wires are of equal length so they will have same resistance and by using H=V2tR⇒H∝1RH = \frac{V^{2}t}{R} \Rightarrow H \propto \frac{1}{R}

⇒ HsHP=RPRs;\frac{H_{s}}{H_{P}} = \frac{R_{P}}{R_{s}}; ⇒ HsHP=R/22R=14\frac{H_{s}}{H_{P}} = \frac{R/2}{2R} = \frac{1}{4}