Question

12 derive an expression for the effective resistance when three resistors are connected in (i) series (ii)

Answer 1

● When the resistors are connected in series .....

Current remains same in each resistor in series connection..

V1 = IR1 ••••••(i)

V2 = IR2 ••••••(ii)

V3 = IR3 ••••••(iii)

Now V = V1 +V2 + V3

FROM EQUATION (i) , (ii) and (iii)

IR = IR1 + IR2 +IR3

IR = I (R1 + R2 + R3)

》[R = R1 + R2 + R3]《

● When the resistors are in parallel....

Potential difference remains the same in parallel connection..

I1 = V/R1•••••••(i)

I2 = V/R2 ••••••(ii)

I3 = V/R3 ••••••(iii)

NOW

I = I1 + I2 + I3

FROM EQUATION (i) , (ii) and (iii),

V/R = V/R1 + V/ R2 + V/ R3

V/ R = V (1/R1 + 1/R2 + 1/R3)

》[1/R = 1/ R1 + 1/ R2 + 1/ R3]《