1)
a) The circuit is kept open for quite some time and then closed at t=0. The circuit shown can be considered to be equivalent to R-C circuit, where the equivalent value of R can be calculated from the series and parallel connection.
When the switch is closed, the voltage in the circuit in R3 begins to grow and is shown in the figure below.
b) Time constant of RC circuit=RC= 80*10-3s(given)
Voltage at time t V(t) is related to voltage at time 0 V(0) by the relation:-
V(t)=V(0)(1-e-t/RC)
Thus at t=20*10-3s
V(t)=V(0)(1-e-20/80)
where V(0)=20 V(given)
Thus, V(t)=20*(1-e-0.25)
V(t)=4.42 V
2)
a) The voltage and current waveforms of a circuit are shown, with current peak at 95 s and Voltage peak at 10 s. Since current lags behind the voltage in the circuit, it is a RL circuit.
b) Here, time period T=1*10-4s(for the waveforms)
Angular frequency =6.28/T=6.28*104rad/s
Further, V/I=5/(0.01)=500(from the graph)
V=IR
Thus, resistance R=V/I=500 ohm
Also, V=IXL
where XL=impedance of RL circuit=L
Thus, inductance L=V/I=8*10-3 H
3) charge on an electron q=1.6*10-19C
magnetic field= Bxi+3Bxj
where i and j are unit vectors along X and Y directions respectively
velocity v=40 i+20 j m/s
Now, Force is given as F=q(vB)
=1.6*10-19(40 i+20 j)(Bxi+3Bxj)=1.6*10-19*100Bx k(along Z-direction)
=1.6*10-17Bx N
The force is given as 8*10-18N
Thus, equating, 1.6*10-17Bx=8*10-18
Bx=0.5 Tesla
For the circuit below, the switch has been open for a long time and is then...
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