Question

Two empty capacitors, C1​ and C2​, are connected in series with R1​. The capacitance of C1​ is 2F, the capacitance of C2​ is 3F, and the resistance R1​ is 5Ω. Calculate the total capacitance of the series combination and the time constant of the resulting RC circuit

Answer 1

The total capacitance of the series combination of two capacitors, C1 = 2F and C2 = 3F, is 1.2F. The time constant of the RC circuit, which includes these capacitors in series with a 5Ω resistor, is 6 seconds.

Step-by-step explanation:

The student asks how to calculate the total capacitance of a series combination of two capacitors and the time constant of the resulting RC circuit. When capacitors are connected in series, the total capacitance (Ctotal) is given by the reciprocal of the sum of the reciprocals of the individual capacitances. Given C1 = 2F and C2 = 3F, we can calculate the total capacitance as

1/Ctotal = 1/C1 + 1/C2
1/Ctotal = 1/2F + 1/3F
1/Ctotal = (3 + 2) / 6F
1/Ctotal = 5/6F
Ctotal = 6/5F = 1.2F

The time constant (τ) of an RC circuit is determined by the formula τ = R * C. In this case, the resistance R1 is given as 5Ω, and we've just calculated the total capacitance to be 1.2F. Thus, the time constant is:

τ = R1 * Ctotal
τ = 5Ω * 1.2F
τ = 6 seconds