A circuit has a resistance of 4k omega, capacitance of 5 mu F, and an EMF of 8V.

Question

A circuit has a resistance of 4k omega, capacitance of 5 mu F, and an EMF of 8V. Determine the following: Maximum current, maximum voltage, and maximum charge The current when the charge is a quarter of its maximum value The charge when the current is a half of its maximum value Current, voltage, and charge at t = RC Time it takes to reach 80% of the maximum voltage across the capacitor Time it takes to reach 75% of the maximum current across the capacitor Time it takes to reach 95% of the maximum energy across the capacitor Time it takes for the voltage across the resistor to reach to 4V after the switch was closed Time it takes the current, voltage and charge across the resistor to discharge to 80% of its initial value after the battery is removed

Explanation / Answer

a)

Maximum current is I = V /R = 8/4000 = 0.002 A or 2 mA

Maximum voltage is V = 8V

Maximum charge Q = CV = (5x10^-6) (8) = 40 x10^-6 C

b)

Q /4 = Q [ 1 -e^(-t /RC) ]

1/4 = 1- e^ (-t /RC)

e^ (-t /RC) = 0.75

t = 5.75 milliseconds

Current

I = 0.002 e ^(-0.0057 / 0.02) = 1.5 mA

c) Io e-t/

Q1= Q [ 1 -e^(-t /RC) ]

d) Io e-1

I = 0.002 (0.3678) = 0.735mA

Q1= Q [ 1 -e^(-1) ]

Q= (40 x10^-6) (1 - 0.3678) = 25.3 micro coulombs or 25.3 x10^-6 coulombs

e)

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