Series-Parallel Circuits
2 February 2005
Series-Parallel Circuits
Objectives
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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
2 February 2005
Professor Andrew H. Andersen
Series-Parallel Circuits
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1
Series-Parallel Circuits
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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
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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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2
Series-Parallel Circuits
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Find RT
RAB = R1 + R4
R 2 R3
R2 + R3
RT = RAC = RAB + RBC
RBC =
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Resistance in the Series-Parallel Circuit
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3
Series-Parallel Circuits
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Resistance in the Series-Parallel Circuit
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Identify the Nodes and Redraw Circuit
Nodes connected
only by a short
are the same node
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Professor Andrew H. Andersen
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4
Series-Parallel Circuits
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Redrawn Circuit from Slide 8
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Current in the Series-Parallel Circuit
• Using the total resistance and the source voltage, find the total
current by applying Ohm’s law
IT =
VS
RT
• 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
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5
Series-Parallel Circuits
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Write the KCL Equation for Node A
ITRAB = I2R2
ITRAB = I3R3
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Apply KCL to Each Node
• At Node B I2 = I3 + I4
• At Node A IT = I1 + I2
• At Node C IT = I1 + I3 + I4
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6
Series-Parallel Circuits
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Apply KVL to the Series-Parallel Circuit
VS = VAB + VBC
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KVL in the Series-Parallel Circuit
VS = VAB + VBC
VBC = VR4 + VR5 = VR3
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7
Series-Parallel Circuits
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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
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Loaded Voltage Dividers
• When a load resistor RL is
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
voltages or currents
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Professor Andrew H. Andersen
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8
Series-Parallel Circuits
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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.
• The typical range for the
Bleeder current is
0.1IRL2 ≤ IR3 ≤ .2IRL2
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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
• Modern digital voltmeters (DMM) have an internal resistance of 10MΩ
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9
Series-Parallel Circuits
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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%
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Analog Voltmeter Loading
In the circuits above, R2 in circuit C is most affected by the
Voltmeter Loading, and least affected by circuit A
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10
Series-Parallel Circuits
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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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Wheatstone Bridge with Transducer Input
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Temperature Transducer
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Balancing the Bridge for 0V Output
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Find All Currents and Voltages
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Find VL for Each Position of the Switch
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