Flenst Ted each question carefully and good luckl 1. In the circuit in figure 1,

Question

Flenst Ted each question carefully and good luckl 1. In the circuit in figure 1, E 4.10kV, c-7.1uF, R, = R2 = R, = 2.02m. with C completely uncharged, switch S is suddenly closed (at t = 0). Ri Rs Figure 1: Question 1 (o) (0 pointe) At t-tt iritor 3 (b) (5 points) What is the potential difference, Vi across the resistor Ri at t-0? (c) (10 points) At t = oc (that is, after many time constants), what is the current ii in resistor 1, current 12 in resistor 2, and current is in resistor 3? a) (6 points) What is the potential diflerence, V, acrus he rei

Explanation / Answer

part a:

when the switch is closed suddenly, the capacitor behaves like a short circui initially.

hence R2 and R3 are connected in parallel.

equivalent resistance=R2*R3/(R2+R3)=2.02*2.02/(2.02+2.02)=1.01 Mega ohms

it is in series with R1.

hence net resistance=R1+1.01=2.02+1.01=3.03 mega ohms

as given that emf is 4.1 kV=4100 volts

voltage E=current*total resistance

==>current=voltage/total resistance=4100/(3.03*10^6)=1.353 mA

current in parallel combination of R2 and R3 is same as current in R1=1.353 mA

as both R2 and R3 are same, current will be divided equally between them

hence current in R2=current in R3=1.353/2=0.6765 mA

part b:

potential difference across R1=current through R1*resistance of R1

=1.353*0.001*2.02*10^6=2733.06 volts

part c:

at t=infinity, the capacitor is saturated and become open circuit

hence there is no current through R3.

i3=0

now R2 and R1 in series.

net resistance in the circuit=2.02+2.02=4.04 mega ohms

then current=emf/resistance

=4100/(4.04*10^6)=1.01485 mA

hence i1=i2=1.01485 mA

part d:

potential difference across R1=current through R1*resistance of R1
=i1*2.02*10^6

=2049.997 volts=2050 volts

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