Sample problems Topic: RC and RL circuits Statement of problem The switch in the circuit in the figure has been in position a for a long time. 8mA27kΩ33kΩab0t=0.25Fμ3kΩ2kΩ4kΩ0iAt t=0, the switch is thrown to position b. (a) Find 0( )itfor t>0. (b) What percentage of the initial energy stored in the capacitor is dissipated in the 4kΩresistor 250sμafter the switch has been thrown? Solution (a) Prior to t=0, the circuit looks like 8mA27kΩ33kΩa0.25FμFirst, the initial voltage on the capacitor is calculated by KVL (0)8(27/ /33)118.8cvmAkkV=×ΩΩ =Then after t=0, the circuit looks like b0.25Fμ3kΩ2kΩ4kΩ0i(0)Cv+−The time constant for the RC circuit is (3/ /(24))0.250.5kkkFmsτμ=ΩΩ +Ω×=Therefore, for t>0, the voltage on the capacitor is ( )(0)exp(/)118.8exp( 2000 )()ccvtvttVτ=−
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