Answer to Question #196023 in Electric Circuits for Asahi

Question

A car battery with a 12-V emf and an internal resistance of 0.050Ω is being charged with a current of 60 A. Note that in this process, the battery is being charged.

(a) What is the potential difference across its terminals? _____ V

(b) At what rate is thermal energy being dissipated in the battery? _____ W

(c) At what rate is electric energy being converted into chemical energy? _____ W

Answer 1

a.) We have $e = 12V$

Internal resistance of the battery $= 0.05 \Omega$

Current $= 60A$

Terminal voltage of the battery $V = e-Ir$

The battery is being charged so, I is now negative:

$V = e + Ir$

$V = 12+(60 \times 0.05) = 15V$

b.) $P_{thermal} = I^2R = (60)^2 \times 0.05 = 180W$

c.) $P = \dfrac{E}{t} = IV$

$P = 60 \times 12 = 720W$

$P_{chemical} = 720-180 = 540W$