When measuring the voltage in a circuit with a meter, it would be nice to assume

Question

When measuring the voltage in a circuit with a meter, it would be nice to assume that the meter has no effect on the circuit. This would be true if no current flowed though it, which means it was like an infinite resistance. In fact real voltmeters always have a small current flowing thourgh them and they behave like they are a large resistance. This resistance is usually called the internal impedance of the meter. Better meters have higher internal impedance and so they disturb the circuit less. The voltage across the 30 kf} resistor in Fig. 28-60 is measured with a voltmeter whose internal impedance is: 30 kOhm (this is a simple old meter); 200 kOhm (this is a better old analog voltmeter); 10 MOhm (this is typical of modern digital multimeters) To two significant figures, what does each read?

Explanation / Answer

40 kohm and 40 kohm are in parallel and their parallel combination is given as

Rp = 40 x 40 / (40 + 40) = 20 kohm

Rp and 30 kohm are in series and their series combination is given as

Rtotal = Rp + 30 = 20 + 30 = 50 kohm

V = Voltage = 100 volts

Current coming from battery is given as

i = V/Rtotal = 100 / 50 = 2 x 10-3 A

Current through 30 kohm = i = 2 x 10-3 A

Voltage across 30 kohm = i R = 2 x 10-3 x 30,000 = 60 V

The current divides equally between two 40 kohm resistances

hence Voltage across each 40 kohm resistors = 100 - 60 = 40 volts

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