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:

Question

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: (A)  2:1  (B)  1:2  (C)  2:9  (D)  9:2

Tardigrade Admin · Accepted Answer

In series, Rs=R+2 R=3 R In parallel, Rp=(R × 2 R/R+2 R) =(2 R2/3 R) =(2/3) R Ratio of heat produced (Hs/Hp) =(Rp/Rs) =((2/3) R/3 R)=(2/9) Hs: Hp =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:

$2 : 1$

$1 : 2$

$2 : 9$

$9 : 2$

In series,
$R_{s} = R + 2 R = 3 R$
In parallel, $R_{p} = \frac{R \times 2 R}{R + 2 R}$
$= \frac{2 R ^{2}}{3 R}$
$= \frac{2}{3} R$
Ratio of heat produced
$\frac{H _{s}}{H _{p}} = \frac{R _{p}}{R _{s}}$
$= \frac{\frac{2}{3} R}{3 R} = \frac{2}{9}$
$H_{s} : H_{p} = 2 : 9$

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