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PhysicsMultiple correct+4 / -2Question 11 of 54

JEE Advanced 2016 · Paper 2, Physics question 11

In the circuit shown below, the key is pressed at time t=0t=0. Which of the following statement(s) is(are) true?

A bridge of four elements: the upper-left arm is a 40 μF capacitor and the lower-left arm a 50 kΩ resistor; the upper-right arm is a 25 kΩ resistor and the lower-right arm a 20 μF capacitor. A voltmeter V joins the top and bottom nodes (− at top, + at bottom). The left and right nodes connect through an ammeter A, a key and a 5 V battery.
Choose one or more options
Answer and worked solution

Official answer: A, B, C, D

The two branches. Both run from the left node (+5 V side) to the right node (0 V):

  • top: 40 μF then 25 kΩ, with τ=1\tau=1 s;
  • bottom: 50 kΩ then 20 μF, with τ=1\tau=1 s.

The voltmeter reads Vbottom−VtopV_{bottom}-V_{top}.

Node voltages.

  • The top node sits across the 25 kΩ resistor: Vtop=5e−tV_{top}=5e^{-t}.
  • The bottom node is 5 V minus the drop across 50 kΩ: Vbottom=5−5e−tV_{bottom}=5-5e^{-t}.

So the reading is 5−10e−t5-10e^{-t}.

  • (A) It is −5 V at t=0t=0 and +5 V as t→∞t\to\infty. True.
  • (B) It is zero when e−t=12e^{-t}=\frac12, i.e. t=ln⁡2t=\ln2 s. True.
  • (C) The ammeter current is (525k+550k)e−t\left(\frac5{25\text{k}}+\frac5{50\text{k}}\right)e^{-t}, which falls to 1/e1/e in 1 s. True.
  • (D) It falls to zero after a long time. True.

(A), (B), (C), (D)

Topics:RC circuits
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