Problem #11 (Due 2/26 Friday by 9:00 a.m.) The rechargeable batteries for a lapt
ID: 1422640 • Letter: P
Question
Problem #11 (Due 2/26 Friday by 9:00 a.m.)
The rechargeable batteries for a laptop computer need a much smaller voltage than what a wall socket provides. Therefore, a transformer is plugged into the wall socket and produces the necessary voltage for charging the batteries.
a) Is the transformer a step-up or a step-down transformer? Explain.
b) Is the current that goes through the batteries greater than, equal to, or smaller than the current coming from the wall socket? Explain.
c) If the transformer has a negligible resistance, is the electrical power delivered to the batteries greater than, equal to, or less than the power coming from the wall socket? Explain.
d) The batteries of a laptop computer are rated at 9.0 V, and a current of 225 mA is used to charge them. The wall socket provides a voltage of 120 V. Determine the ratio of turns of the primary coil to the secondary coil for this transformer.
e) What is the current coming from the wall socket?
f) Find the power delivered by the wall socket and the power sent to the batteries.
Explanation / Answer
a) The transformer must be a step-down transformer.
Because it needs much smaller voltage than what a wall socket provides.
b) current that goes through the batteries greater than than the current coming from the wall socket
because, P_socket = P_battery
V_socket_I_socket = V_socket*I_battery
I_battery = (V_socket/V_battery)*I_socket
we know, V_socket > V_battery
===> I_battery > I_socket
c) equalto. As there is no power loss the total power is delivered to the battery.
d) N_primary/N_secondary = V_primary/V_seconary
= 120/9
= 13.33
e) I_socket = I_battery*(V_battery/V_socket)
= 225 mA*(9/120)
= 16.875 mA
f) Power deliver by by the wall socket and the power sent to the batteries = 225*16.875*10^-3
= 3.796 W
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