Answer to Question 6

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An analogue voltmeter is known to be accurately calibrated.  A digital voltmeter of infinite resistance measures the voltage across a 150 kW resistor as 3.5 V, but when the analogue meter is used, the voltage is measured as 1.4 V.  Calculate the resistance of the meter.

Work out the current with the perfect voltmeter:

I = 3.5 V 150 103 W = 23.3 10-6 A

 

Treat the voltmeter as a perfect voltmeter in parallel with an unknown resistor, R.   Assume that the current to the parallel resistors remains constant.

The current through the 150 kW resistor is now:

I = 1.4 V 150 103 W = 9.33 10-6 A

 

The current through the voltmeter resistor = 23.3 10-6 A - 9.33 10-6 A  = 13.9 10-6 A

 

R = 1.4 V 13.9 10-6 A = 100 000 W