Question

Immediately after the switch is closed, determine the value of the charge Qon the capacitor, the voltage Von the capacitor. Also, find the current ithrough the 20-Ω resistor (R3) that is in parallel with the capacitor. Make sure you clearly explain your reasoning.

Answer 1

Answer:

See explanation.

Explanation:

Immediately after the switch is closed the capacitor, which was initially discharged, has had not enough time to collect any charge; therefore, the charge on the capacitor is zero.

Also, since there is no charge on the capacitor, there is no potential difference (voltage) across the capacitor immediately after the switch is closed.

Going around the circuit gives

$(1). \: \: V- IR_1-I_2R_3-IR_2 =0,$

where $I$ is the current through resistors $R_1$, $R_2$, and $I_3$ is the current through $R_3$.

Now since there is no potential across the capacitor, the current is not divided at the junction; therefore, $I_2 =I$, which gives

$(1). \: \: V- IR_1-IR_3-IR_2 =0,$

$I = \dfrac{V}{R_1+R_2+R_3}$

$I = \dfrac{120V}{20\Omega+20\Omega+20\Omega }$

$\boxed{I =2A}$

which is the current through $R_3$ immediately after the switch is closed.