Question

A battery has an emf of 15.0 V. The terminal voltage of the battery is 12.2 V when it is delivering 26.0 W of power to an external load resistor R. (a) What is the value of R? Ω (b) What is the internal resistance of the battery?

Answer 1

Answer:

(a) 5.725 Ω

(b) 1.3 Ω

Explanation:

(a)

E = emf of the battery = 15.0 Volts

V = terminal voltage of the battery = 12.2 Volts

P = Power delivered to external load resistor "R"  = 26.0 W

R = resistance of external load resistor

Power delivered to external load resistor is given as

$P = \frac{V^{2}}{R}$

26.0 = 12.2²/R

R = 5.725 Ω

(b)

r = internal resistance of the battery

i = current coming from the battery

Power delivered to external load resistor is given as

P = i V

26.0 = i (12.2)

i = 2.13 A

Terminal voltage is given as

V = E - ir

12.2 = 15 - (2.13) r

r = 1.3 Ω