In the circuit shown, E= 1.2 kV, C= 6.5 microfarads, R1=R2=R3=0.73M. With C comp

Question

In the circuit shown, E= 1.2 kV, C= 6.5 microfarads, R1=R2=R3=0.73M. With C completely uncharged, switch S is suddenly closed at (t=0)

Please show the math clearly, thank you!!

1. In the circuit of Fig. shown below, = 1.2 kV, C 6.5 F,R1 R2 R3 = 0.73 M With C completely uncharged, switch S is suddenly closed (at t -0) At t-0, what are (a) current i in resistor l, (b) current i2 in resistor 2, (c) current i in resistor 3? At t = oo (that is, after many time constants), what are (d) i, (e) i2, (f) i3? What is the potential difference V2 across resistor 2 at (g) t 0 and (h) e? Ri Rs Ro

Explanation / Answer

at t = 0 ,

potential diff across C will be zero.

so we can remove capacitor and can consider a simple plain wire instead of it.

now R2 and R3 are in parallel connection,

1/R' = 1/R2 + 1/R3 = 1/0.73 + 1/0.73

R'= 0.365 M ohm

Req = R' + R1 = 0.365 + 0.73 = 1.095 M ohm

current through battery, I = e / Req = (1.2 kV ) / (1.095)

    = 1.10 mA

a) current through R1 = 1.10 mA

B) current through R2 = 1.10/2 = 0.55 mA

C) current through R3 = 0.55 mA

d) at inifinity, no current will flow through capacitor.

so current through battery and R1 = (1.2 kV) / (0.73 + 0.73)Mohm

i1 = 0.822 mA

e) i2 = 0.822 mA

f) i3 = 0

g) at t = 0

V = i2R2 = 0.55 m A x 0.73 M ohm = 0.40 kV

h) at t= infinite

V = i2R2 = 0.822 x 0.73 = 0.60 kV

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