If an ammeter A reads 2 A and the voltmeter V reads 20 V, what is the value of resistance R? (Assuming finite

Question

If an ammeter A reads 2 A and the voltmeter V reads 20 V, what is the value of resistance R? (Assuming finite resistances of ammeter and voltmeter)

Accepted Answer

1.  **Measurement Setup:** In the standard voltmeter-ammeter method to measure an unknown resistance $R$, the voltmeter is connected in parallel with the resistor to measure the potential difference ($V$), and the ammeter is connected in series to measure the current ($I$).
2.  **Finite Resistance:** A real voltmeter has a finite (though large) resistance $R_V$ . Therefore, when connected in parallel with $R$, it draws a small amount of current ($I_V$) to produce the deflection.
3.  **Current Analysis:** The ammeter, being in the main line, measures the total current supplied to the parallel combination of the resistor and the voltmeter. Thus, the ammeter reading is $I_{measured} = I_R + I_V$, where $I_R$ is the true current through the resistor.
4.  **Resistance Calculation:** The apparent or measured resistance is calculated using Ohm's law: $R_{measured} = \frac{V}{I_{measured}} = \frac{20}{2} = 10\ \Omega$.
5.  **Comparison:** Since the measured current $I_{measured}$ ($I_R + I_V$) is greater than the true current $I_R$, the denominator in the resistance formula is larger than it should be for the true resistance.
    $R_{true} = \frac{V}{I_R}$.
    Since $I_{measured} > I_R$, it follows that $R_{measured} < R_{true}$.
    Therefore, $10 < R_{true}$. The true resistance is greater than $10\ \Omega$.

Step-by-Step Solution

Practice All PHYSICS Questions