Question

Two identical resistors, each of resistance 10ohm are connected in series and in parallel to volt cell.Calculate the ratio of powers in each case

Answer 1

Hey.

We have :

Two identical resistors each 10 ohm.

Let V be the potential difference of the cell.

Equivalent resistance :

In series : Rs = r1 + r2

so, Rs = 10 + 10 = 20 ohm

In parallel :

1/Rp = 1/r1 + 1/r2

=> Rp = (r1.r2 / r1+r2 )

so, Rp = (10×10 / 10+10) = 100/20 = 5 ohm

Now, As Power = V^2/ R

So, Ps = V^2/20

& Pp = V^2/5

Hence , Ratio, Ps/Pp = (V^2/20)/(V^2/5)

= 5/20 = 1/4

Hence , Ps : Pp = 1 : 4

Thanks.