Capacitors and Resistors Initially, the switch is in position \'\'a\'\', and the

Question

Capacitors and Resistors

Initially, the switch is in position ''a'', and the capacitor is fully charged to voltage Va. 1. (3 pts) The switch is switched to position ''b''. How long does it take the capacitor's volt age to drop to 0.25Va? (Use the symbols defined in the circuit diagram needed.) 2. (3 pts) When the capacitor's voltage reaches 0.25V, the switch is switched back to position ''a''. How long does it take the capacitor's voltage rise to 0.85Va? 3. (2 pt) Find the numeric answers* to part 1 if R1 = 11 kohm, R2 = 51 kohm, and C = 47muF. 4. (2 pt) Find tile numeric answer to part 2 using tile same values of R1, R2, and C.

Explanation / Answer

a)

Time Constant

T=R2C

In a RC circuit Voltage as a function of time for discharging is given by

V=Vae-t/T

0.25Va=Vae-t/T

Ln(0.25)=-t/T

t=-(R2C)*Ln(0.25)

b)

Time Constant

T=(R1+R2)C

The Voltage it needed to rise from 0.25Va to 0.85Va

V=(0.85-0.25)Va=0.6Va

In a RC circuit Voltage as a function of time for charging is given by

V=Vo[1-e-t/T]

0.6=1-e-t/T

t=-(R1+R2)C*Ln(0.4)

c)

Time Constant

T=R2C =(51*103)(47*10-6)

T=2.4 s

so

t=-2.4*Ln(0.25)

t=3.32 s

d)

Time Constant

T=(R1+R2)C =(11+51)*103*(47*10-6)

T=2,9 s

so

t=-ln(0.4)*2.9

t=2.67 s

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