Answer to Question #164685 in Electric Circuits for Elizabeth

Question

A car battery with a 12-V emf and an internal resistance of0.050 Ω is being charged with a current of60 A. Note that in this process, the battery is being charged.(a) What is the potential difference across its terminals?(b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted in to chemical energy?

Answer 1

Given,

EMF of battery, $E=12\text{ volts }$

Internal resistance, $r=0.05\Omega$

Current, $i=60A$

(A) As the battery is being charged, The voltage across battery is-

$V=E+ir$

$\Rightarrow V=12+60(0.05)\\=12+3\\=15\text{ volts}$

(B) Thermal power dissipation-

$P_{ther.}=i^2r$

$=(60)^2\times 0.05\\=3600\times 0.05\\=180W$

(C) Power delivered to battery, $P=VI$

$=12\times 60\\=720W$

Rate at which electrical energy converted into chemical energy-

$P_{chem.}=P-P_{therm.}$

$=720-180\\=540W$