An electrical circuit having combinations of resistances and capacitan

An electrical circuit having combinations of resistances and capacitance is given below. The current, flowing through the circuit will be

1 A
2 A
1·5 A
0·5 A
This question was previously asked in
UPSC CDS-2 – 2022
The circuit consists of a 10V DC voltage source, a 10 ohm resistor, a 20 ohm resistor, and a 10 µF capacitor. We are asked for the current flowing through the circuit. In a DC circuit with a capacitor, after the capacitor has been fully charged (steady state), no current flows through the branch containing the capacitor.
– The diagram shows the 10 ohm resistor in series with a parallel combination.
– The parallel combination consists of two branches: one with the 20 ohm resistor and the capacitor in series, and another branch which appears to be a simple wire (zero resistance).
– In steady state DC, the capacitor acts as an open circuit, meaning the branch containing the 20 ohm resistor and capacitor has effectively infinite resistance to DC current flow.
– The other branch in parallel has zero resistance (a wire).
– Current always follows the path of least resistance. In parallel, a zero-resistance path effectively shorts out any parallel path with resistance. Thus, all the current passing through the 10 ohm resistor will flow through the wire branch, and no current will flow through the branch containing the 20 ohm resistor and capacitor in steady state.
– The equivalent resistance of the parallel combination is 0 ohms.
– The total resistance of the circuit is the sum of the series resistor and the equivalent parallel resistance: R_total = 10 ohms + 0 ohms = 10 ohms.
– The total current flowing from the battery is given by Ohm’s Law: I = V / R_total = 10V / 10 ohms = 1 A. This is the current flowing through the circuit from the battery.
The 20 ohm resistor and the capacitor only influence the current flow during the transient phase when the capacitor is charging. Once the capacitor is fully charged in DC steady state, its branch becomes effectively open circuit, and the parallel wire branch carries all the current.