Two identical wires are first connected in series and then in parallel. The amount of heat produced in both the conditions are in the ratio of:

Question

Two identical wires are first connected in series and then in parallel. The amount of heat produced in both the conditions are in the ratio of: (A) 1: 2 (B) 2: 1 (C) 1: 4 (D) 4: 1

Tardigrade Admin · Accepted Answer

Resistance in series combination is more than resistance in parallel combination.
The amount of heat produced across a wire when current

i

is

H = i^{2} Rt

Where

R

is resistance of wire.
In series equivalent resistance is

R_{s} = R + R = 2 R

In parallel, equivalent resistance is

R_{p} = \frac{R}{2}

.

∴ \frac{H _{s}}{H _{p}} = \frac{2 R}{R /2} = 4

∴ H_{s} : H_{p} = 4 : 1

Q. Two identical wires are first connected in series and then in parallel. The amount of heat produced in both the conditions are in the ratio of:

1 : 2

2 : 1

1 : 4

4 : 1