In the circuit in (Figure 1) , switch 1 has been in position a and switch 2 has
ID: 2990665 • Letter: I
Question
In the circuit in (Figure 1) , switch 1 has been in position a and switch 2 has been closed for a long time. At t=0, switch 1 moves instantaneously to position b. Two hundred microseconds later, switch 2 opens, remains open for 600 ?s, and then recloses.
Find vo 1 ms after switch 1 makes contact with terminal b if vs = 11V .
In the circuit in (Figure 1) , switch 1 has been in position a and switch 2 has been closed for a long time. At t=0, switch 1 moves instantaneously to position b. Two hundred microseconds later, switch 2 opens, remains open for 600 ?s, and then recloses. Find vo 1 ms after switch 1 makes contact with terminal b if vs = 11V .Explanation / Answer
switch 1 is in position a and switch 2 is closed.
so capacitor is fully charged.
hence it will be open circuit.
net current=11/(5+5+30)=0.275 mA
voltage across capacitor=0.275*30=8.25 volts
now at t=0,
switch 1 moves to b.
the capacitor will start discharging.
net resistance across capacitor=(15*30)/(15+30)=10 kilo ohms
time constant=10*25=250 micro seconds
hence the voltage across capacitor at any time t :
8.25*exp(-t/250) where t is micro seconds
so after 200 micro seconds, the switch 2 opens.
voltage across capacitor at t=200 micro seconds is:3.707 volts
now the time constant becomes:15*25=375 micro seconds
so voltage across caapcitor=3.707*exp(-(t-200)/375)
at t=600 micro seconds,voltage across capacitor=0.7484 volts
as it recloses, the new voltage equation:0.7484*exp(-(t-800)/250)
so at t=1 ms, i.e. after 200 micro seconds after the swtich 2 recloses:
voltaae acroaa capacitor=0.3363 volts
so applying voltage division:
10*0.3363/15=0.2242 volts