Engineering Science EAB_S_127 Electricity Chapter 3

Introduction  Potentiometers  Voltage dividers  Measurement of electrical resistance  The Wheatstone bridge

Potentiometers  When a resistive material is connected at both ends to a voltage source and a sliding bar is moved along its length, a variable voltage is output depending on the resistance  These devices are commonly called “Potentiometers” and are typically used in volume controls on audio equipment V in V out 0V0V

Potentiometers continued  It can be shown that the voltage across the bar is a fraction of the input voltage depending on the ratio of the input and output resistances.  Hence as I is the same for the entire resistive strip, Ohm’s Law shows us that + V out - R in I V in R out Sliding bar

Potentiometers: Example  Calculate R out when we require an output voltage of 10V from a voltage divider, which has the total resistance of 100 Ω and can supply the maximum voltage 50 V.  Answer:  Hence

Voltage Dividers  Consider the circuit shown in Figure 3.2 below containing two discrete resistors. We can develop an equation that describes the voltage across each resistor R 1 and R 2 in terms of the input voltage and a ratio of resistors + V in - ITIT R2R2 R1R1 Figure 3.2 Potential Divider - V V 2 +

Voltage Dividers: Example  Calculate V 1 and V 2 when V in = 24V, R 1 = 8 Ω and R 2 = 40 Ω  Answer:

The Wheatstone Bridge  We use an “Ohmmeter” to measure an unknown resistance  The heart of the simplest Ohmmeter is a so-called “Wheatstone Bridge” circuit  If R 1 was a variable resistor, we can adjust it until V ab = 0

The Balanced Wheatstone Bridge  When V ab = 0, a special condition occurs: the bridge is said to be “balanced”, i.e. V a = V b  This implies that i g = 0, hence from KCL, i 4 = i 3 and i 2 = i 1  Further, from Ohm’s Law; i 4 R 4 = i 2 R 2 and i 3 R 3 = i 1 R 1

The Wheatstone Bridge continued  Hence

The Wheatstone Bridge: Example  Calculate R 1 in a Wheatstone bridge when it is balanced and when R 2 = 300 Ω, R 3 = 200 Ω, R 4 = 100 Ω.  Answer:

Summary  Learning Outcomes:  Potentiometers  Voltage dividers  Wheatstone Bridge  Balanced Condition