Question

Consider an RC circuit with E = 12.0 V ,R = 165 Ω , and C = 55.6 μF .

A) Find the time constant for the circuit.

B) Find the maximum charge on the capacitor.

C) Find the initial current in the circuit.

Answer 1

For RC circuit, we have given that :

voltage of the battery, = V = 12 V

resistance, R = 165

capacitance, C = 55.6 x 10^-6 F

(A) the time constant for the circuit is given as :

= RC                                            { eq.1 }

inserting the values in above eq.

= (165 ) (55.6 x 10^-6 F)

= 9174 x 10^-6 sec

= 9.17 x 10^-3 sec

Or = 9.17 ms

(B) the maximum charge on the capacitor is given as :

Q_max = C V                                       { eq.2 }

inserting the values in eq.2,

Q_max = (55.6 x 10^-6 F) (12 V)

Q_max = 667.2 x 10^-6 C

Q_max = 667.2 C

(C) the initial current in the circuit which is given as :

using an ohms law,     V = I R

or    I = V / R                                                    { eq.3 }

inserting the values in eq.3,

I = (12 V) / (165 )

I = 0.0727 A

I = 72.7 x 10^-3 A

Or    I = 72.7 mA