A battery with voltage V1 and internal resistance R1 is connected through a swit

Question

A battery with voltage V1 and internal resistance R1 is connected through a switch S1 to an

electrical circuit consisting of 4 resistors R2;R3;R4;R5, as shown in the circuit diagram below.

1. Find the equivalent resistance R2345 of the circuit attached to the battery. Write your answer

symbolically in terms of R2;R3;R4;R5.

2. What current is drawn from the battery when the switch is closed? Write your answer in

terms of R2345, R1, and V1.

3. Use your answers from parts 1 and 2 to calculate the equivalent resistance R2345 of the circuit

attached to the battery and the current drawn from the battery for the following values:

V1 = 6:0 V

R1 = 49:9 ohm

R2 = 90:9 k ohm

R3 = 43:2 ohm

R4 = 1:00 k ohm

R5 = 2:00 k ohm

4. An uncharged capacitor is inserted in series between the battery and the circuit. What is the

time constant of this RC circuit? Write your answer in terms of R2345, R1, and the capacitor's

capacitance C.

5. For C = 1000 uF, calculate the current drawn by the RC circuit from the battery at the

following times: (a) immediately after the switch is closed; (b) 100 seconds after the switch is

closed.

Pleaes show all formulas and explain in detail. Thanks

A battery with voltage V1 and internal resistance R1 is connected through a switch S1 to an electrical circuit consisting of 4 resistors R2;R3;R4;R5, as shown in the circuit diagram below.

Explanation / Answer

a) equivaelnt resistance (Req)= R2 || ( R3 + R4||R5)) = 1/( 1/R2 + (R4 + R5)/(R3*R4 + R4*R5 + R5*R3))

b) when the switch is closed

current = V/ (R1 + Req) {Req is as calcuated in part a) }

c) Req = 1/(1/90900 + (1000+2000)/(1000*2000 + 1000*43.2 + 2000*43.2 )) = 704.366 ohm

current = 6 / (704.366 + 49.9) = 7.955 mA

d) time constant = (Req + R1) * C = (R1 + 1/( 1/R2 + (R4 + R5)/(R3*R4 + R4*R5 + R5*R3))) * C

e)Let Req + R1 = Ro

i(t) = V/Ro (1 - e^(-t / RoC))

at t = 0

i = V/Ro

after 100seconds

i(t) = V/Ro (1 - e^(-100 / 0.001Ro)) = V/Ro (1 - e^(-100000 / Ro))

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