A 12.0 V battery has an internal resistance of 0.24 and a capacity of 50.0Ah. Th

ID: 1779174 • Letter: A

Question

A 12.0 V battery has an internal resistance of 0.24 and a capacity of 50.0Ah. The battery is charged by passing a 30-A current through it for 1.7 h.

Part A) What is the terminal voltage during charging?

Part B) What total electrical energy is supplied to the battery during charging?

Part C) What electrical energy is dissipated in the internal resistance during charging?

Part D) The battery is now completely discharged through a resistor, again with a constant current of 30 A. What is the external circuit resistance?

Part E) What total electrical energy is supplied to the external resistor?

Part F) What total electrical energy is dissipated in the internal resistance?

Part G) Why are the answers to parts (b) and (e) not the same?

a) E = 12 V, r = 0.24 ohm, Q = 50.0 A.h = 50 * 3600 = 180000 C

terminal voltage during charging = E + I r

= 12 + (30 * 0.24) = 19.2 V

b) total electrical energy is supplied = V I * t = 19.2 * 30 * (1.7 * 3600)

= 3.525 * 106 J

c) electrical energy is dissipated = I2 * r t = 302 * 0.24 * (1.7 * 3600)

= 1.32 * 106 J

d)external circuit resistance R = E/I - r = (12 / 30) - 0.24

= 0.16 ohm

e) td = Q / I = 180000 / 30 = 6000 s

total electrical energy = 302 * 0.16 * 6000

= 8.64 * 105 J

f) total electrical energy is dissipated in the internal resistance = I2 r td

= 302 * 0.24 * 6000 = 1.29 * 106 J

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