. A 500-Ω resistor, an uncharged 1.50-μF capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the RC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?

Explanation:

Given an RC circuit to analyze

R=500Ω

C=1.50-μF uncharged

Emf(V)=6.16V

Series connection

a. Initial current, since the capacitor is initially uncharged then, the voltage appears at the resistor

Using ohms law

V=iR

Then, i=V/R

i=6.16/500

i=0.01232 Amps

i=12.32 mA.

b. The time constant is given as

τ=RC

τ=500×1.5×10^-6

τ=0.00075second

τ=0.75 ms

c. What is current after 1 time constant

Current in a series RC circuit is given as

Time after I time constant is

t=1 ×τ

t= τ

i=V/R exp(-t/RC)

Where RC= τ

i=V/Rexp(-t/ τ)

i=6.16/500exp(-1), since t= τ

i=0.004532A

I=4.532mA

d. Voltage after one time constant

Voltage of a series RC circuit(charging) is given as

Again, t= τ

V=Vo(1 - exp(-t/ τ)),

V=6.16(1-exp(-1))

V=6.16(1-0.3679)

V=6.16×0.632

V=3.89Volts

V=3.89V

V=

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