Two wires have resistances R and 2 R . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is:

Question

Two wires have resistances R and 2 R . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is: (A) 2: 1 (B) 1: 2 (C) 2: 9 (D) 9: 2

Tardigrade Admin · Accepted Answer

In series combination, the net resistance

R_{s} = R + 2 R = 3 R

Heat produced in

R_{s}

,

H_{s} = \frac{V ^{2}}{R _{s}} = \frac{V ^{2}}{3 R} ... (i)

In parallel combination, the net resistance

R_{p} = \frac{R \times 2 R}{R + 2 R} = \frac{2 R ^{2}}{3 R} = \frac{2}{3} R

Heat produced in

R_{p}

H_{p} = \frac{V ^{2}}{R _{p}} = \frac{V ^{R}}{2 R /3} = \frac{3 V ^{2}}{2 R} ... (ii)

Dividing Eq. (i) by Eq. (ii), we obtain

\frac{H _{s}}{H _{p}} = \frac{V ^{2} /3 R}{3 V ^{2} /2 R} = \frac{2}{9}

Q. Two wires have resistances $R$ and $2 R$ . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is:

2 : 1

1 : 2

2 : 9

9 : 2

Q. Two wires have resistances R and 2R . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is:

2 : 1

1 : 2

2 : 9

9 : 2

Q. Two wires have resistances $R$ and $2 R$ . When both are joining in series and in parallel, then ratio of heats generated in these situations on applying the same voltage, is: