In the given RC circuit containing 10 V and 20 V sources, resistors 2 Ω, 3 Ω and 6 Ω and a 2 μF capacitor, find the ratio of the time constant with switch S open to that with S closed. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

In the given RC circuit containing 10 V and 20 V sources, resistors 2 Ω, 3 Ω and 6 Ω and a 2 μF capacitor, find the ratio of the time constant with switch S open to that with S closed. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Time constant τ = RₜₕC, where Rₜₕ is the resistance seen by capacitor with both ideal voltage sources shorted. Step 2 — With S open, the capacitor sees 2 Ω in series with 6 Ω, giving Rₜₕ = 8 Ω. Step 3 — With S closed, the 6 Ω and 3 Ω form a parallel combination: 6∥3 = 2 Ω. Therefore Rₜₕ = 2 + 2 = 4 Ω. Step 4 — τ(open)/τ(closed) = 8/4 = 2.