The circuit shown has a 40 Volt battery, R_1 = 600000 Ohms, R_2 = 400000 Ohms, a

Question

The circuit shown has a 40 Volt battery, R_1 = 600000 Ohms, R_2 = 400000 Ohms, and a capacitor with C = 5 times 10^-5 F. At time t = 0 the switch is turned on. (a) Knowing that items in parallel have the same voltage and that the capacitor starts uncharged, what current will flow onto the capacitor just after the switch is turned on? (b) Knowing that the capacitor will eventually reach a full charge and no more current will flow through the capacitor, what voltage will the capacitor and R_2 have across them? (c) Noticing that the charge that flows through the capacitor has to come through R_1 but not R_2, roughly how much time do you think it might take the capacitor to charge up to 63% of its final voltage?

Explanation / Answer

(a) Just after the switch is turned on, the capacitor will act as a short circuit. So, all the current that passes through R1 goes through the capacitor and none through R2. So, the effective circuit is R1 and the battery.

So, Current passing through the capacitor, I = V/R1 = 40 / 600000 = 6.67 * 10-5 A

(b) When fully charged, the capacitor acts as an open circuit and no current passes through it.

So, the effective circuit is R1 and R2 in series and the battery,

Current in the circuit, I = V/(R1 + R2) = 40 / (600000 + 400000) = 4 * 10-5 A

Voltage across R2 and capacitor, V = IR2 = (4 * 10-5) * (4 * 105) = 16 V

(c) The time it takes for the capacitor to charge up to 63% of its final voltage is called the time constant of the circuit.

So, time taken = time constant of the circuit = RthevC

Now, to find thevenin resistance (Rthev) in series with the capacitor, we remove the battery from the circuit and calculate the net resistance across the capacitor.

So, Rthev = parallel combination of R1 and R2

=> Rthev = R1R2 / (R1 + R2) = 400000 * 600000 / (400000 + 600000) = 2.4 * 105 ohm

So, time constant = (2.4 * 105) * (5 * 10-5) = 12 s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.