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 I0 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 I1 = 0 as there is no current through the capacitor at steady state.




Now, as they are in parallel



Note that Vaf 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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