Question

A full wave rectifier circuit with diodes ($D_1$) and ($D_2$) is shown in the figure. If input supply voltage $V_{in}$ = 220sin (100 $\pi$ t) volt, then at t = 15 msec

• A. $D_1$ is forward biased, $D_2$ is reverse biased
• B. $D_1$ is reverse biased, $D_2$ is forward biased
• C. $D_1$ and $D_2$ both are forward biased
• D. $D_1$ and $D_2$ both are reverse biased

Answer 1

Answer: (B)

(2) $D_1$ is reverse biased, $D_2$ is forward biased

Answer 2

To determine the biasing state of the diodes $D_1$ and $D_2$ at $t = 15 \text{ msec}$, we need to analyze the input voltage at that specific time.

1. Analyze the input supply voltage: The input supply voltage is given by $V_{in} = 220 \sin(100 \pi t)$ volt. We need to find the sign of $V_{in}$ at $t = 15 \text{ msec}$.

2. Calculate the phase angle at $t = 15 \text{ msec}$: Substitute $t = 15 \text{ msec} = 15 \times 10^{-3} \text{ s}$ into the argument of the sine function: Phase angle $\theta = 100 \pi t = 100 \pi (15 \times 10^{-3}) = 1.5 \pi$ radians.

3. Determine the sign of $V_{in}$: Now, evaluate $\sin(\theta) = \sin(1.5 \pi) = \sin(270^\circ) = -1$. Therefore, $V_{in} = 220 \times (-1) = -220 \text{ volt}$.

4. Analyze the transformer and secondary coil polarity: Since $V_{in}$ is negative at $t = 15 \text{ msec}$, it implies that the top terminal of the primary winding is negative with respect to the bottom terminal. Assuming a standard transformer winding (dots on the same side), the phase relationship dictates that:

   • The top end of the secondary coil (connected to the anode of $D_1$) will be negative with respect to the center tap.
   • The bottom end of the secondary coil (connected to the anode of $D_2$) will be positive with respect to the center tap.

   Let the center tap be at 0 V (ground).

   • Potential at the anode of $D_1$ is negative (e.g., $-V_s$, where $V_s$ is the peak voltage across half the secondary winding).
   • Potential at the anode of $D_2$ is positive (e.g., $+V_s$).
   • The cathodes of both $D_1$ and $D_2$ are connected to the load resistor $R_L$, which is connected to the center tap. The output voltage across $R_L$ is always positive (or zero) in a full-wave rectifier. So, the common cathode point will be at a positive potential (or zero) relative to the center tap.

5. Determine the biasing of diodes $D_1$ and $D_2$:

   • Diode $D_1$:

     • Anode is at a negative potential.
     • Cathode is at a positive (or zero) potential (output voltage).
     • Since the anode potential is less than the cathode potential ($V_A < V_K$), diode $D_1$ is reverse biased.

   • Diode $D_2$:

     • Anode is at a positive potential.
     • Cathode is at a positive (or zero) potential (output voltage).
     • Since the anode potential is greater than the cathode potential ($V_A > V_K$), diode $D_2$ is forward biased.

Therefore, at $t = 15 \text{ msec}$, $D_1$ is reverse biased and $D_2$ is forward biased.