Question

Two resistors have resistances R(smaller) and R(larger), where R(smaller) < R(larger). When the resistors are connected in series to a 12.0-V battery, the current from the battery is 1.52 A. When the resistors are connected in parallel to the battery, the total current from the battery is 10.5 A. Determine the two resistances.

Answer 1

let us assume smaller resistance is 'S' and and larger resistance is 'R.'

When the resistors are connected in series:

equivalent resistance = (R + S);

V = I*(R + S);

(R + S) = V/I = 12/1.52 = 7.894 ..............................................(1)

similarlly,

When the resistors are connected in parallel to the battery

equivalent resistance = R*S /(R + S);

R*S /(R + S) = V/I = 12/10.5 = 1.1428 ........................................(2)

By solving equation (2) and (1)

S = 1.3859 ohm and R = 6.508 ohm.