Question

Two identical resistors are connected in parallel across a 27-V battery, which supplies them with a total power of 6.9 W. While the battery is still connected, one of the resistors is heated so that its resistance doubles. The resistance of the other resistor remains unchanged. Find (a) the initial resistance of each resistor, and (b) the total power delivered to the resistors after one resistor has been heated.

Answer 1

Given , P = 6.9 W , V = 27V

a) Initially ,

Equivalent resistance of the circuit initially is,

R_eq = R * R / ( R + R) = R/2

Now ,

P = V² / R_eq = 2 V² / R

R = 2 * 27 * 27 / 6.9

R = 211.304 ? is the value of each resistor initially.

(b) After one resistor has been heated.

R_1new = 2 R and R₂ = R

Equivalent resistance of the circuit is :

R_eq = R₁ * R₂ / ( R₁ + R₂)

R_eq = 2R * R / (2R + R) = (2/3) R

R_eq = (2/3)*211.304 = 140.87 ?

Thus, total power delivered to the resistors now is,

P = V² / R_eq

P = 27 * 27 / 140.87

P = 5.175 W