You have a 76.1-mF capacitor initially charged to a potential difference of 10.9

Q: You have a 76.1-mF capacitor initially charged to a potential difference of 10.9

A. Time constant is given by: Tau = RC tau = 3.01*76.1*10^-3 = 0.229 sec tau = 0.23 sec B. In RC circuit Voltage is given by: V = Vo*(1 - exp(-t/tau)) When V = 2.81 V, then 2.81 = 10.9*(1 - exp(-t/0.23)) exp(-t/0.23) = 1 - 2.81/10.9 = 0.742 exp(-t/0.23) = 0.742 take log both side t = -0.23*ln 0.742 t = 0.069 sec t = (0.069/0.23)*tau = 0.3*tau multiple of time constant = 0.3

ID: 2030921 • Letter: Y

Question

You have a 76.1-mF capacitor initially charged to a potential difference of 10.9 V. You discharge the capacitor through a 3.01- resistor. What is the time constant? After what multiple of the time constant does the potential difference reach 2.81 V?

You have a 76.1-mF capacitor initially charged to a potential difference of 10.9 V. You discharge the capacitor through a 3.01-2 resistor. What is the time constant? After what multiple of the time constant does the potential difference reach 2.81 V? Time constant: Number Multiple of time constant: Number

Explanation / Answer

Time constant is given by:

Tau = RC

tau = 3.01*76.1*10^-3 = 0.229 sec

tau = 0.23 sec

In RC circuit Voltage is given by:

V = Vo*(1 - exp(-t/tau))

When V = 2.81 V, then

2.81 = 10.9*(1 - exp(-t/0.23))

exp(-t/0.23) = 1 - 2.81/10.9 = 0.742

exp(-t/0.23) = 0.742

take log both side

t = -0.23*ln 0.742

t = 0.069 sec

t = (0.069/0.23)*tau = 0.3*tau

multiple of time constant = 0.3

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You have a 76.1-mF capacitor initially charged to a potential difference of 10.9

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