GATE EC 2016 Set 3 — Question 42
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Network Theory → Transient & AC Analysis → RL, RC & RLC Transients
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Question
Assume that the circuit in the figure has reached the steady state before time when the resistor suddenly burns out, resulting in an open circuit. The current (in ampere) at is __________
Correct answer
0.98 to 1.02
Solution
1.Steady State Analysis at :
- In steady state, capacitors act as open circuits.
- The total resistance of the circuit is .
- The total current from the source is .
- The voltage at the top node of the bridge is .
- The voltage at the right junction (between the and resistors) is .
- Since no current flows through the bridge resistor (), the voltage at the left junction (between the capacitors) is .
- The initial voltages across the capacitors are:
- At , the resistor burns out, creating an open circuit in that branch.
- Capacitors maintain their voltages instantaneously: and .
- Consequently, and .
- The current flows from node to node through the bridge resistor.
- Since the branch is open, the top-right resistor and the bridge resistor are now in series between and .
- .
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