a) When the switch is closed, calculate the effective resistance R12345 of the c

Question

a) When the switch is closed, calculate the effective resistance R12345 of the circuit in termsofR1 =2?,R2 =1?,R3 =3?,R4 =4?,andR5 =4?. Show a symbolic answer (4 points) and a numerical value (1 point).

b) If the battery voltage is V =6.0 V, what is the current drawn?

c) What is the current through R1?

d) Now a capacitor with capacitance C = 2000?F is inserted in the circuit between the battery and the switch. What is the time constant of the circuit?

e) If the capacitor starts out uncharged, what is the current drawn 15 ms after the switch is closed?

Explanation / Answer

a)

R2 and R3 are in series

R_23=R_2+R_3=1+3=4 ohms

R4 and R5 are in parallel

1/R_45=1/R_4 +1/R_5 =1/4 +1/4

R_45=2 ohms

R_1 and R_23 are in parallel

1/R_123=1/R_1 +1/R_23 =1/2 +1/4

R_123 =1.33 ohms

R_123 and R_45 are in parallel ,so equivalent resistance

R_12345=R_123 +R_45 =1.33+2

R_12345=3.33 ohms

b)

I=V/R_12345=6/3.33

I=1.8 A

c)

I1=I*(R23/R1+R23)=1.8*(4/2+4)

I1=1.2 A

d)

Time Constant

T=RC =3.33*2000*10-6

T=6.67*10-3 s or 6.67 ms

e)

In a RC Circuit current as a function of time is given by

I=Io[1-e-t/T]=1.8[1-e-15/6.67]

I=1.61 A

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