How Does a Voltmeter Measure Voltage in a Circuit with Internal Resistance?

In summary, a voltmeter measures voltage by using a coil of wire in a magnetic field, while analog and digital voltmeters differ in their display methods and accuracy. It cannot measure current or resistance, but some multimeters have this capability. The internal resistance of a voltmeter can affect its readings, so it is designed with high resistance. It is important to use the correct range on a voltmeter for accurate measurements.
  • #1
viperassasin
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0

Homework Statement



A voltmeter with resistance R_V is connected across the terminals of a battery of emf EMF and internal resistance r. Find the potential difference V_meter measured by the voltmeter.

Homework Equations



v=IR Vab= Va -Vb

The Attempt at a Solution



tried using equations with epsolon.
 
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  • #2
Just go in a loop around the circuit, and re-arrange for Vf-Vi
 
Last edited:
  • #3


A voltmeter is a device used to measure the potential difference, or voltage, between two points in an electrical circuit. In order to understand how a voltmeter works, we must first understand the concept of voltage.

Voltage, symbolized by V, is a measure of the electric potential energy per unit charge. It is often referred to as the "pressure" or "force" that drives the flow of electric current in a circuit. The unit of voltage is the volt (V).

A voltmeter works by measuring the voltage difference between two points in a circuit. In the homework statement given, the voltmeter is connected across the terminals of a battery with emf EMF and internal resistance r. This means that the voltmeter is connected in parallel with the battery.

When a voltmeter is connected in parallel, it will have the same potential difference as the points it is connected across. This is because parallel connections have the same potential difference across them. Therefore, the potential difference measured by the voltmeter, V_meter, will be the same as the potential difference of the battery, V_battery.

To calculate V_battery, we can use the equation V_battery = EMF - Ir, where EMF is the electromotive force of the battery and Ir is the voltage drop across the internal resistance of the battery. This equation is derived from the Kirchhoff's loop rule, which states that the sum of the voltage drops in a closed loop in a circuit must equal the sum of the voltage sources in that loop.

Substituting this into the equation for V_meter, we get V_meter = EMF - Ir. This means that the voltmeter will measure a slightly lower potential difference than the actual emf of the battery, due to the voltage drop across the internal resistance of the battery.

In conclusion, a voltmeter works by measuring the potential difference between two points in an electrical circuit. When connected in parallel, it will have the same potential difference as the points it is connected across. By using the equation V_meter = EMF - Ir, we can calculate the potential difference measured by the voltmeter in a circuit with a battery and internal resistance.
 

1. How does a voltmeter measure voltage?

A voltmeter measures voltage by using a coil of wire that is placed in a magnetic field. When voltage is applied to the coil, it produces a current which creates a magnetic field that interacts with the original field. This interaction causes the needle on the voltmeter to move, indicating the voltage.

2. What is the difference between an analog and a digital voltmeter?

An analog voltmeter uses a needle to indicate the voltage on a scale, while a digital voltmeter displays the voltage as a numerical value on a screen. Analog voltmeters are more prone to human error and have a limited range, while digital voltmeters are more accurate and have a wider range of measurement.

3. Can a voltmeter be used to measure current or resistance?

No, a voltmeter can only measure voltage. To measure current, an ammeter is needed, and to measure resistance, an ohmmeter is needed. However, some multimeters have the capability to measure all three quantities.

4. How does the internal resistance of a voltmeter affect its readings?

The internal resistance of a voltmeter can affect its readings by creating a voltage drop in the circuit being measured. This means that the voltmeter itself will use some of the voltage being measured, resulting in a slightly lower reading. To minimize this effect, voltmeters are designed with high internal resistance.

5. Why is it important to use the correct range on a voltmeter?

Using the correct range on a voltmeter is important because it ensures the most accurate measurement. If the range is set too high, the voltmeter may not have enough sensitivity to detect small changes in voltage. On the other hand, if the range is set too low, the voltmeter may become overloaded and give an incorrect reading.

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