Question

Two identical resistors are first connected in series and then in parallel. 1) Find the ratio of equivalent resistance in 2 cases. 2) Compare the heat produced by the combination of resistors in 2 cases.

Answer 1

Let the resistor be R
so when connected in series :
R + R = 2R

When connected in parallel :
1/R + 1/R = 2/R = R/2
Ratio = 2R / (R/2)= 4:1

Heat produced when in series :
I^2R T = I^2 2RT

Heat produced when in parallel:
I^2 R T = I^2 R/2T

so heat produced in series combination is 4 times than heat produced in parallel

Answer 2

1) when connected in series:

R+R=2R

2) when connected in parallel:

1/R+1/R=2/R

R=R/2

so, ratio=2R/R/2=4:1