This question asks about the Peak Inverse Voltage (PIV) across a diode when it is not conducting in a bridge rectifier circuit. The PIV is the maximum voltage a diode can withstand when reverse-biased without breaking down.

Understanding Bridge Rectifier Operation

A bridge rectifier uses four diodes to convert alternating current (AC) to direct current (DC). It provides a full-wave rectified output, meaning it utilizes both the positive and negative halves of the AC input cycle.

Let the AC input voltage be represented by \( V_{in} = V_p \sin(\omega t) \), where \( V_p \) is the peak voltage.

The bridge rectifier configuration consists of four diodes (let's label them D1, D2, D3, D4). During each half-cycle of the AC input, two diodes conduct current through the load, while the other two diodes are reverse-biased and block the current.

Analyzing PIV During Conduction Cycles

We need to determine the voltage across the diodes that are *not* conducting (reverse-biased).

Positive Half-Cycle Analysis

During the positive half-cycle of the AC input, the voltage is positive (e.g., terminal X is positive relative to terminal Y). In a standard bridge rectifier configuration, diodes D1 and D3 conduct.

• Current flows from the positive AC terminal (X), through D1, through the load (from P to Q), through D3, and back to the negative AC terminal (Y).
• Diodes D2 and D4 are reverse-biased and block the current.

Let's examine the voltage across one of the non-conducting diodes, say D4:

• Diode D4 has its anode connected to the positive AC terminal (X) and its cathode connected to the negative output terminal (Q).
• The potential at terminal X can reach \( +V_p \) during the peak of the positive half-cycle.
• The potential at terminal Q is connected via the conducting diode D3 to the negative AC terminal (Y). Assuming ideal diodes, the voltage drop across D3 is zero. Therefore, the potential at Q is approximately the potential at Y.
• During the positive half-cycle, the potential at Y is at its minimum (0V if we consider the peak-to-peak voltage).
• The voltage across the reverse-biased diode D4 is \( V_{D4} = V_{Anode(D4)} - V_{Cathode(D4)} \).
• This voltage is approximately \( V_X - V_Y \).
• At the peak of the positive half-cycle, \( V_X = V_p \) and \( V_Y = 0 \).
• Therefore, the voltage across D4 is \( V_{D4} \approx V_p - 0 = V_p \).

The peak voltage appearing across the non-conducting diode D4 is equal to the peak input voltage, \( V_p \).

Negative Half-Cycle Analysis

During the negative half-cycle of the AC input, the voltage is negative (e.g., terminal Y is positive relative to terminal X). Diodes D2 and D4 conduct.

• Current flows from the positive AC terminal (Y), through D2, through the load (from Q to P), through D4, and back to the negative AC terminal (X).
• Diodes D1 and D3 are reverse-biased and block the current.

Let's examine the voltage across one of the non-conducting diodes, say D1:

• Diode D1 has its anode connected to the positive AC terminal (X) and its cathode connected to the positive output terminal (P).
• The potential at terminal X is now at its minimum (0V).
• The potential at terminal P is connected via the conducting diode D2 to the positive AC terminal (Y). Assuming ideal diodes, the voltage drop across D2 is zero. Therefore, the potential at P is approximately the potential at Y.
• During the negative half-cycle, the potential at Y can reach \( +V_p \).
• The voltage across the reverse-biased diode D1 is \( V_{D1} = V_{Anode(D1)} - V_{Cathode(D1)} \).
• This voltage is approximately \( V_X - V_P \).
• Substituting the potentials, \( V_{D1} \approx V_X - V_Y \).
• At the peak of the negative half-cycle, \( V_X = 0 \) and \( V_Y = V_p \).
• Therefore, the voltage across D1 is \( V_{D1} \approx 0 - V_p = -V_p \).

The magnitude of the peak voltage appearing across the non-conducting diode D1 is \( |-V_p| = V_p \).

Conclusion on PIV

In both half-cycles, the peak inverse voltage across the diodes that are not conducting is equal to the peak value of the AC input voltage (\( V_p \)).

Therefore, the PIV of a non-conducting diode in a bridge rectifier is the peak value of a.c. input.