Q. 805.0( 2 Votes )

# The switch S shown in figure is kept closed for a long time and is then opened at t = 0. Find the current in the middle 10 Ω resistor at t = 1.0 ms.

Concepts/Formulas used:

When is capacitor is discharging through as resistor of resistance R, the current through the resistor is given by:

where I_{0} is the initial current and C is the capacitance of the capacitor.

Answer :

When the switch is closed and the circuit is in steady state, no current passes through the capacitor.

Applying Kirchhoff’s loop rule on loop bedcb,

Substitute I_{1} = 0 as there is no current through the capacitor at steady state.

Now, as they are in parallel

Note that V_{af} is the potential difference across the capacitor.

When the switch is just opened, the potential difference across it is the same for a moment as the charge and capacitance is the same. However, the charge and potential decrease slowly as the capacitor starts discharging.

Discharging:

We know that when discharging,

Applying Kirchhoff’s loop rule on fabef,

At , and

Here, R = 10Ω and C = 25μF

Now,

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HC Verma - Concepts of Physics Part 2