A capacitor C = 100 μF is connected to three resistors, each 1 kΩ, and a 9 V battery as shown. Switch S was closed for a long time, then opened. The discharge time constant is 10x ms. Find x.
Physics · Mixed Chapter
JEE Mains

Question

A capacitor C = 100 μF is connected to three resistors, each 1 kΩ, and a 9 V battery as shown. Switch S was closed for a long time, then opened. The discharge time constant is 10x ms. Find x.

G1 Physics · Accepted Answer

Step 1 — Find discharge path after opening S: After the battery is disconnected, the charged capacitor discharges through two 1 kΩ resistors in parallel, as shown in the source figure. Step 2 — Equivalent resistance: 1/Rₑᵩ = 1/1000 + 1/1000 ⇒ Rₑᵩ = 500 Ω. Step 3 — RC time constant: τ = RₑᵩC = 500×100×10⁻⁶ = 0.050 s = 50 ms. Step 4 — Identify x: The question states τ = 10x ms, so 10x = 50 ⇒ x = 5. Answer: 5.