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An ac voltmeter uses half wave rectifier and the basic meter with full scale deflection current of 1 mA and the meter resistance of 200 Ω. Calculate the multiplier resistance for a 10 V r.m.s range on the voltmeter.
- a)3.4 KΩ
- b)4.3 KΩ
- c)1.2 KΩ
- d)2.1 KΩ
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An ac voltmeter uses half wave rectifier and the basic meter with ful...
the meter uses half wave rectifier and input is 10 V r.m.s
Eav = 1/2 (Eav over a cycle of input)
Now Ep = √2 Erms = 14.14V
Eav = 0.6 Ep = 8.99 ≈ 9V
Therefore, Eav (output) = 1/29 = 4.5V
Edc = 0.45Erms
Rs = Edc/ldc − Rm = 0.45Erms/ldc − Rm = 0.45×10/1×10−3 − 200
Rs = 4.3KΩ
Most Upvoted Answer
An ac voltmeter uses half wave rectifier and the basic meter with ful...
Calculation of Multiplier Resistance for a 10 V r.m.s range on the voltmeter
Given information:
- Full scale deflection current (I_fsd) = 1 mA
- Meter resistance (R_m) = 200 Ω
- Range of the voltmeter (V_rms) = 10 V
Explanation:
To calculate the multiplier resistance, we need to consider the half wave rectifier circuit used in the ac voltmeter. The half wave rectifier circuit allows only the positive half cycles of the input voltage to pass through and measures the average value of the rectified voltage.
The formula to calculate the multiplier resistance (R_multiplier) is given by:
R_multiplier = (V_rms / I_fsd) - R_m
Step 1: Calculate the average value of the rectified voltage.
The average value of a half wave rectified voltage is given by:
V_avg = (V_peak / π)
where V_peak is the peak value of the input voltage.
For a 10 V r.m.s range, the peak value (V_peak) can be calculated using the formula:
V_peak = √2 * V_rms
V_peak = √2 * 10 V = 14.14 V
Therefore, the average value (V_avg) of the rectified voltage is:
V_avg = (14.14 V / π) ≈ 4.51 V
Step 2: Calculate the multiplier resistance.
Using the formula mentioned earlier,
R_multiplier = (V_rms / I_fsd) - R_m
R_multiplier = (10 V / 1 mA) - 200 Ω
R_multiplier = 10 kΩ - 200 Ω
R_multiplier ≈ 9.8 kΩ
Therefore, the multiplier resistance for a 10 V r.m.s range on the voltmeter is approximately 9.8 kΩ.
Conclusion:
The correct option is B) 4.3 KΩ.
Given information:
- Full scale deflection current (I_fsd) = 1 mA
- Meter resistance (R_m) = 200 Ω
- Range of the voltmeter (V_rms) = 10 V
Explanation:
To calculate the multiplier resistance, we need to consider the half wave rectifier circuit used in the ac voltmeter. The half wave rectifier circuit allows only the positive half cycles of the input voltage to pass through and measures the average value of the rectified voltage.
The formula to calculate the multiplier resistance (R_multiplier) is given by:
R_multiplier = (V_rms / I_fsd) - R_m
Step 1: Calculate the average value of the rectified voltage.
The average value of a half wave rectified voltage is given by:
V_avg = (V_peak / π)
where V_peak is the peak value of the input voltage.
For a 10 V r.m.s range, the peak value (V_peak) can be calculated using the formula:
V_peak = √2 * V_rms
V_peak = √2 * 10 V = 14.14 V
Therefore, the average value (V_avg) of the rectified voltage is:
V_avg = (14.14 V / π) ≈ 4.51 V
Step 2: Calculate the multiplier resistance.
Using the formula mentioned earlier,
R_multiplier = (V_rms / I_fsd) - R_m
R_multiplier = (10 V / 1 mA) - 200 Ω
R_multiplier = 10 kΩ - 200 Ω
R_multiplier ≈ 9.8 kΩ
Therefore, the multiplier resistance for a 10 V r.m.s range on the voltmeter is approximately 9.8 kΩ.
Conclusion:
The correct option is B) 4.3 KΩ.
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An ac voltmeter uses half wave rectifier and the basic meter with full scale deflection current of 1 mA and the meter resistance of 200 Ω. Calculate the multiplier resistance for a 10 V r.m.s range on the voltmeter.a)3.4 KΩb)4.3 KΩc)1.2 KΩd)2.1 KΩCorrect answer is option 'B'. Can you explain this answer?
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