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A 250000 ohm a 750000 ohm resistor are connected in series across a 75 volt source. (a) Determine the error in measuring the voltage across each of these resistance when the voltage is read with a 0-150 volt, 1000 ohm-per-voltmeter. (b) Determine the error in measuring the voltage across each of these resistance when read with a 0-75 volt, 20000 ohms-per-voltmeter ?
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A 250000 ohm a 750000 ohm resistor are connected in series across a 75...
Determination of Error in Measuring Voltage Across Resistors
Given
Resistance 1 (R1) = 250000 Ω
Resistance 2 (R2) = 750000 Ω
Source voltage (V) = 75 V
Voltmeter 1 (VM1): Range = 0-150 V, Sensitivity = 1000 Ω/V
Voltmeter 2 (VM2): Range = 0-75 V, Sensitivity = 20000 Ω/V
Calculations
For Voltmeter 1 (VM1)
Equivalent resistance (Req) = R1 + R2 = 250000 + 750000 = 1000000 Ω
Total current (I) = V/Req = 75/1000000 = 0.000075 A
Voltage across R1 = IR1 = 0.000075 x 250000 = 18.75 V
Voltage across R2 = IR2 = 0.000075 x 750000 = 56.25 V
As VM1 has a sensitivity of 1000 Ω/V, the current through the voltmeter is 18.75/1000 = 0.01875 A for R1 and 56.25/1000 = 0.05625 A for R2.
Error in measuring voltage across R1 = 0.01875 x 1000 = 18.75 mV
Error in measuring voltage across R2 = 0.05625 x 1000 = 56.25 mV
For Voltmeter 2 (VM2)
As the range of VM2 is 0-75 V, it cannot measure the voltage across R2 directly as it is greater than the range of the voltmeter.
Voltage across R1 remains the same as calculated above.
Current through R2 = I - IR1 = 0.000075 - 0.00005625 = 0.00001875 A
Voltage across R2 = IR2 = 0.00001875 x 750000 = 14.0625 V
As VM2 has a sensitivity of 20000 Ω/V, the current through the voltmeter is 14.0625/20000 = 0.000703125 A for R2.
Error in measuring voltage across R1 = 0.01875 x 20000 = 375 mV
Error in measuring voltage across R2 = 0.000703125 x 20000 = 14.0625 mV
Explanation
When a voltmeter is connected in parallel across a resistor, it draws a small amount of current from the circuit which causes a voltage drop across the voltmeter. This voltage drop introduces an error in the measurement of the voltage across the resistor. The amount of error depends on the sensitivity and the internal resistance of
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A 250000 ohm a 750000 ohm resistor are connected in series across a 75 volt source. (a) Determine the error in measuring the voltage across each of these resistance when the voltage is read with a 0-150 volt, 1000 ohm-per-voltmeter. (b) Determine the error in measuring the voltage across each of these resistance when read with a 0-75 volt, 20000 ohms-per-voltmeter ?
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