A battery with an emf of 10.8 V and internal resistance of 1.07 carries a positi
ID: 1517317 • Letter: A
Question
A battery with an emf of 10.8 V and internal resistance of 1.07 carries a positive current of 0.485 A from its negative terminal to its positive terminal.
(a) How long is required for 1.09 C of charge to pass through the battery?
(b) By how much will the electrical potential energy of 1.09 C of charge increase in crossing the battery terminals?
(c) By how much will the chemical energy decrease?
(d) How much electrical power is supplied by the battery?
(e) At what rate is chemical energy used?
Please show work and units, thank you!
Explanation / Answer
a) I = dQ/dt
==> dt = dQ/I
= 1.09/(0.485)
= 2.247 s
b)
when current flows potentail difference between the terminals,
v = V_emf - I*rin
= 10.8 - 0.485*1.07
= 10.28 volts
change in potential energy, dU = q*dV
= 1.09*10.28
= 11.2 J
c) decrease in chemical energy = dU + increase in thermal energy
= 11.2 + I^2*rin
= 11.2 + 0.485^2*1.07
= 11.45 J
d) power supplied by the battery, P = dU/dt
= 11.2/2.247
= 4.98 W
e) rate of chemical energy use = 11.45/2.247
= 5.096 w
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