Electrical measurements

Voltage sources

imageBatteries and other voltage sources have internal resistance.  When they do work moving charges against the electric force, some of this work is already converted to thermal energy in the battery.  The amount of energy lost to thermal energy in the battery is Ir, where I is the current flowing in the circuit and r is the internal resistance of the battery.  The voltage across the battery terminals therefore drops from the nominal value V to (V - Ir) when a current is flowing in the circuit.  In a circuit diagram we represent the internal resistance of the battery by a resistor r connected in series with the emf.

Electrical Measurements

A voltmeter is a device used to measure voltages, while an ammeter measures currents.  Meters are either analog or digital devices.  Analog meters show the output on a scale with a needle, while digital devices produce a digital readout.  Analog voltmeters and ammeters are both based on a device called a galvanometer.  Digital voltmeters and ammeters generally determine the voltage drop across a known resistor and then convert the result to a digital value for display.


Resistors in parallel have the same voltage across them.  If you want to measure the voltage across a circuit element, such as a resistor, you place the voltmeter in parallel with the resistor.  The voltmeter is shown in a circuit diagram as a V in a circle, and it acts as another resistor.  To prevent the voltmeter from changing the current in the circuit (and therefore the voltage across the resistor), the voltmeter must have a resistance much larger than that of the resistor.  If the resistance of the voltmeter is large, only a negligible current flows through the meter.


Resistors in series have the same current flowing through them.  An ammeter, must be placed in series with a resistor to measure the current through the resistor.  On a circuit diagram, an ammeter is shown as an A in a circle.  The ammeter acts as a resistor.  To prevent the ammeter from changing the current in the circuit, the ammeter must have a very small resistance compared to the resistance R of the circuit.


An ohmmeter uses an internal battery to send a known current through the resistor.  The ohmmeter then measures the voltage across the resistor, and displays the resistance R = V/I.  The resistor must be disconnected from the rest of the circuit.