All the elements in the circuit shown in the following figure are ideal. Which of the following statements is/are true?
\begin{center}
\includegraphics[width=0.65\textwidth]{21.jpeg}
\end{center}
Show Hint
- When switch \(S\) is ON, both \(D_1\) and \(D_2\) conduct and \(D_3\) is reverse biased
- When switch \(S\) is ON, \(D_1\) conducts and both \(D_2\) and \(D_3\) are reverse biased
- When switch \(S\) is OFF, \(D_1\) is reverse biased and both \(D_2\) and \(D_3\) conduct
- When switch \(S\) is OFF, \(D_1\) conducts, \(D_2\) is reverse biased and \(D_3\) conducts
The Correct Option is B, C
Solution and Explanation
Step 1: Case when switch \(S\) is ON.
- The 2A current source is directly connected across the 20V source.
- The voltage at the junction tends to rise such that diode \(D_1\) becomes forward biased.
- Diode \(D_2\) sees higher potential at its cathode (20V) compared to anode (10V), hence reverse biased.
- Diode \(D_3\) sees higher potential at its cathode (40V) than anode (20V), hence reverse biased.
Thus, when \(S\) is ON:
\[
D_1 \, \text{conducts}, D_2 \, \text{OFF}, D_3 \, \text{OFF}
\]
This matches option (B).
Step 2: Case when switch \(S\) is OFF.
- The 2A current source is no longer shorted; it tries to push current.
- \(D_1\) has 20V at its anode and higher potential at cathode side due to current source, so it becomes reverse biased.
- Current from 10V source and 20V source flows through \(D_2\) (anode at 10V, cathode at 20V → forward biased).
- Similarly, path through \(D_3\) (anode at 20V, cathode at 40V → forward biased).
Thus, when \(S\) is OFF:
\[
D_1 \, \text{OFF}, D_2 \, \text{ON}, D_3 \, \text{ON}
\]
This matches option (C).
Step 3: Eliminate wrong options.
- (A) claims \(D_1\) and \(D_2\) conduct with \(S\) ON — incorrect since \(D_2\) is reverse biased.
- (D) claims \(D_1\) and \(D_3\) conduct with \(S\) OFF — incorrect since \(D_1\) is OFF.
Final Answer:
\[
\boxed{(B) \; \text{and} \; (C)}
\]
Questions Asked in GATE EE exam
In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage \( E \) for unit change in the resistance \( R \), in V/Ω, is __________ (round off to two decimal places).
- GATE EE - 2025
- Electrical Energy, Power
- A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as the cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume a linear magnetic circuit. The external resistance in ohms that must be connected in series with the armature to reduce the speed of the motor by half is closest to:
- GATE EE - 2025
- Instrument transformers
- The input voltage \( v(t) \) and current \( i(t) \) of a converter are given by, \[ v(t) = 300 \sin(\omega t) \, {V} \] \[ i(t) = 10 \sin\left(\omega t - \frac{\pi}{6}\right) + 2 \sin\left(3\omega t + \frac{\pi}{6}\right) + \sin\left(5\omega t + \frac{\pi}{2}\right) \, {A} \] where \( \omega = 2\pi \times 50 \) rad/s. The input power factor of the converter is closest to:
- Instrument(s) required to synchronize an alternator to the grid is/are:
- GATE EE - 2025
- Electrical Energy, Power
The relationship between two variables \( x \) and \( y \) is given by \( x + py + q = 0 \) and is shown in the figure. Find the values of \( p \) and \( q \). Note: The figure shown is representative.
- GATE EE - 2025
- Algebra