Ammeters and Voltmeters* An ammeter measures current; a voltmeter measures voltage. Both are based on galvanometers, unless they are digital. The current in a circuit passes through the ammeter; the ammeter should have low resistance so as not to affect the current. Figure 26-28. An ammeter is a galvanometer in parallel with a (shunt) resistor with low resistance, Rsh.

Example : Ammeter design. Design an ammeter to read 1.0 A at full scale using a galvanometer with a full-scale sensitivity of 50 μA and a resistance r = 30 Ω. Check if the scale is linear. Solution: When the current is 1 A, 50 μA should flow through the ammeter. The shunt resistor is in parallel with the galvanometer; using Ohm’s law we find that the shunt resistance should be 1.5 x 10-3 Ω. The scale will be linear as long as the current does not affect the resistance.

A voltmeter should not affect the voltage across the circuit element it is measuring; therefore its resistance should be very large. Figure 26-29. A voltmeter is a galvanometer in series with a resistor with high resistance, Rser.

Example : Voltmeter design. Using a galvanometer with internal resistance 30 Ω and full-scale current sensitivity of 50 μA, design a voltmeter that reads from 0 to 15 V. Is the scale linear? Solution: When the voltage across the galvanometer is 15V, there should be 50 μA of current flowing through it. Using Ohm’s law, we find the series resistance should be 300 kΩ. The scale will again be linear.

An ohmmeter measures resistance; it requires a battery to provide a current. Figure 26-30. An ohmmeter.

Summary: An ammeter must be in series with the current it is to measure; a voltmeter must be in parallel with the voltage it is to measure.

Example: Voltage reading vs. true voltage. Suppose you are testing an electronic circuit which has two resistors, R1 and R2, each 15 kΩ, connected in series as shown in part (a) of the figure. The battery maintains 8.0 V across them and has negligible internal resistance. A voltmeter whose sensitivity is 10,000 Ω/V is put on the 5.0-V scale. What voltage does the meter read when connected across R1, part (b) of the figure, and what error is caused by the finite resistance of the meter? Solution: On the 5-V scale, the meter has a resistance of 50,000 Ω. The equivalent resistance of the meter and R1 in parallel is 11.5 kΩ. The total resistance of the circuit is 26.5 kΩ, so the current is 0.30 mA; the voltage across R1 (and therefore also across the voltmeter) is 3.5 V. Without the voltmeter, the voltage across R1 is half the battery voltage, or 4.0 V; this is more than a 10% error.

Summary of Chapter A source of emf transforms energy from some other form to electrical energy. A battery is a source of emf in parallel with an internal resistance. Resistors in series:

Resistors in parallel: Kirchhoff’s rules: Sum of currents entering a junction equals sum of currents leaving it. Total potential difference around closed loop is zero.

RC circuit has a characteristic time constant: To avoid shocks, don’t allow your body to become part of a complete circuit. Ammeter: measures current. Voltmeter: measures voltage.