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A 120 V, 30 Hz source feeds a half wave rectifier circuit through a 4 : 1 step down transformer, the average output voltage is
- a)30 V
- b)13.5 V
- c)10 V
- d)7.07 V
Correct answer is option 'B'. Can you explain this answer?
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A 120 V, 30 Hz source feeds a half wave rectifier circuit through a 4 ...
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Given data:
- Source voltage (V_s) = 120 V
- Frequency (f) = 30 Hz
- Step-down transformer turns ratio (N) = 4:1
The half-wave rectifier circuit converts the AC input voltage into a pulsating DC output voltage. In this case, the input voltage is being fed through a step-down transformer before being rectified.
1. Calculation of the transformer output voltage:
The turns ratio of the transformer is given as 4:1. This means that the secondary voltage (V_s') is one-fourth of the primary voltage (V_s).
V_s' = (1/N) * V_s
V_s' = (1/4) * 120 V
V_s' = 30 V
The output voltage of the transformer is 30 V.
2. Calculation of the rectified output voltage:
In a half-wave rectifier circuit, only the positive half cycles of the input voltage are rectified. The negative half cycles are suppressed.
The average output voltage of a half-wave rectifier is given by:
V_avg = V_m/π
Where V_m is the peak value of the rectified voltage.
In this case, the input voltage is 30 V. The peak value of the rectified voltage is equal to the peak value of the input voltage.
V_m = V_s' = 30 V
V_avg = V_m/π
V_avg = 30 V/π
V_avg ≈ 9.55 V
The average output voltage of the half-wave rectifier circuit is approximately 9.55 V.
3. Rounding to the nearest option:
The options provided are:
a) 30 V
b) 13.5 V
c) 10 V
d) 7.07 V
Among these options, the closest value to the calculated average output voltage of 9.55 V is option b) 13.5 V.
Therefore, the correct answer is option b) 13.5 V.
- Source voltage (V_s) = 120 V
- Frequency (f) = 30 Hz
- Step-down transformer turns ratio (N) = 4:1
The half-wave rectifier circuit converts the AC input voltage into a pulsating DC output voltage. In this case, the input voltage is being fed through a step-down transformer before being rectified.
1. Calculation of the transformer output voltage:
The turns ratio of the transformer is given as 4:1. This means that the secondary voltage (V_s') is one-fourth of the primary voltage (V_s).
V_s' = (1/N) * V_s
V_s' = (1/4) * 120 V
V_s' = 30 V
The output voltage of the transformer is 30 V.
2. Calculation of the rectified output voltage:
In a half-wave rectifier circuit, only the positive half cycles of the input voltage are rectified. The negative half cycles are suppressed.
The average output voltage of a half-wave rectifier is given by:
V_avg = V_m/π
Where V_m is the peak value of the rectified voltage.
In this case, the input voltage is 30 V. The peak value of the rectified voltage is equal to the peak value of the input voltage.
V_m = V_s' = 30 V
V_avg = V_m/π
V_avg = 30 V/π
V_avg ≈ 9.55 V
The average output voltage of the half-wave rectifier circuit is approximately 9.55 V.
3. Rounding to the nearest option:
The options provided are:
a) 30 V
b) 13.5 V
c) 10 V
d) 7.07 V
Among these options, the closest value to the calculated average output voltage of 9.55 V is option b) 13.5 V.
Therefore, the correct answer is option b) 13.5 V.
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