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in Physics by (23.9k points)

A perfect voltmeter and a perfect ammeter are connected in turn between

points E and F of a circuit whose diagram is shown in Fig. 96. The readings of the instruments are U0 and I0.

Determine the current I through the resistor of resistance R connected between points E and F.

1 Answer

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Best answer

We shall mentally connect in series two perfect (having zero internal resistance) current sources of emf's equal to -U6 . and U0 between points A and F. Obviously, this will not introduce any change in the circuit. The dependence of the current through the resistor of resistance R on the emf's of the sources will have the form

where ξ is the emf of the source contained in the circuit, and the coefficients α and β depend on the resistance of the circuit.

If we connect only one perfect source of emf equal to - U0 between A and F, the potential difference between A and B will become zero. Therefore, the first two terms in the equation for I will be compensated: I = βU0. The coefficient β is obviously equal to 1/(R + Reff), where Reff is the resistance between A and B when the resistor R is disconnected. This formula is also valid for the case R = 0, which corresponds to the connection of the ammeter. In this case,

Consequently, the required current is

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