Question

unlike the idealized voltmeter, a real voltmeter has a resistance that is not infinitely large. part a a voltmeter with resistance $r_v$ is connected across the terminals of a battery of emf $\mathcal{e}$ and internal resistance $r$. find the potential difference $v_{meter}$ measured by the voltmeter. view available hint(s) $v_{meter}=$ submit part b complete previous part(s)

Explanation:

Step1: Find the total current in the circuit

The total resistance of the circuit is the sum of the internal - resistance of the battery $r$ and the resistance of the voltmeter $R_V$, i.e., $R_{total}=r + R_V$. According to Ohm's law $I=\frac{\mathcal{E}}{R_{total}}$, so the current in the circuit is $I=\frac{\mathcal{E}}{r + R_V}$.

Step2: Calculate the potential difference across the voltmeter

The potential difference across the voltmeter $V_{meter}$ is given by Ohm's law $V = IR$, where $R = R_V$ and $I=\frac{\mathcal{E}}{r + R_V}$. So $V_{meter}=I\times R_V=\frac{\mathcal{E}R_V}{r + R_V}$.

Answer:

$\frac{\mathcal{E}R_V}{r + R_V}$