Series-Parallel Circuits. Objectives

Series-Parallel Circuits

Objectives

• Identify series-parallel configuration • Analyze series-parallel circuits

• Apply KVL and KCL to the series-parallel circuits • Analyze loaded voltage dividers

• Determine the loading effect of a voltmeter on a circuit • Analyze a Wheatstone bridge circuit

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Analysis of Series-Parallel Circuits

• Determine total resistance seen by the source

• Determine all branch currents and the source current • Determine all voltage drops

Total Resistance

• Identify the parallel resistances, and calculate the equivalent resistance(s)

• Identify the series resistance, and calculate the total resistance for the circuit

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Find R

R = R + R

R R

R =

R + R

R = R = R + R

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Resistance in the Series-Parallel Circuit

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Redrawn Circuit from Slide 8

Current in the Series-Parallel Circuit

• Using the total resistance and the source voltage, find the total current by applying Ohm’s law

• Using the current-divider formula, Kirchhoff’s current law (KCL), Ohm’s law, or combinations of these, you can find the current in any branch of a series-parallel circuit

S T T V I = R

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Write the KCL Equation for Node A

Apply KCL to Each Node

• At Node B I

= I

+ I

• At Node A I

= I

+ I

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Apply KVL to the Series-Parallel Circuit

KVL in the Series-Parallel Circuit

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Unloaded Voltage Dividers

• A voltage divider produces an output which depends upon the values of the dividing resistors

• All resistors in an unloaded voltage divider are

connected in series • This voltage is the

unloaded output voltage

Loaded Voltage Dividers

• When a load resistor RLis

connected between the output terminal and ground, the output voltage is

reduced by an amount that depends on the value of RL

• Solve the circuit for RT

between node A and ground. • Then solve for the desired

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Load Current and Bleeder Current

• Bleeder current is the current left (I3) after the

total load current is subtracted from the total current into the circuit • In Power Supply circuits, R3

is used to discharge the filter capacitor when power is removed.

Loading Effect of a Voltmeter

• When measuring across a resistor, a voltmeter is connected in parallel with the resistor

• Being in parallel, the internal resistance of the voltmeter will have a loading effect on the circuit that is being measured

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Loading Effect of a Voltmeter

• If the meter resistance is at least one hundred times greater than the resistance across which it is connected, the loading effect can be neglected

– the measurement error is less than 1%

Analog Voltmeter Loading

In the circuits above, R2in circuit C is most affected by the

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Wheatstone Bridge

• A Wheatstone bridge is used to precisely measure resistance

• A Wheatstone bridge is also applied with transducer measurements, to measure physical quantities such as temperature, strain, and pressure, where small transducer resistance changes may need to be precisely measured

– Tiny changes in transducer resistance will unbalance the bridge, thereby providing a measurement reading

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Temperature Transducer

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Find All Currents and Voltages