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DC Circuit Analysis
HRW P639>
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Circuit Symbols Resistor
Voltage source (battery)
Switch (open)
Wire (Conductor)
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What is a circuit? A basic circuit comprises:
• Voltage source (ex. battery)
• Load (ex. Resistors)• Conductor (ex. Wires)
• Control (ex. Switch)
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DC Circuit Analysis
DC Circuits are analyzed in 3 models• Series resistors
•Parallel resistors• Combination resistors
Circuit Analysis investigates:• Equivalent resistance
• Circuit current in/out battery• Voltage drop across components
• Current through components
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DC Circuit Analysis - Series
Components are
connected “nose-tail” or
inline There is only one path
for the circuit current (I)
to flow.
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Examples of series circuits
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Circuit Analysis - Series
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DC Circuit Analysis – Series
Equivalent (or total) resistance
• RT = R1 + R2 + R3
Current is the same through allcomponents = circuit current (I)
Voltage drop across each resistor (n)
• Vn = I*Rn • Sum of voltage drops = battery voltage
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DC Circuit Analysis – Series
Practice
Analyze the series circuit by
calculating:
• Equivalent resistance RT
• Circuit current (I) flowing
into/out of the battery
• Voltage drop across the 3, 4
and 5 ohm resistor
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DC Circuit Analysis - Parallel
Components areconnected “side by side”
There are multiple paths
for the current to flow,splitting into branch currents through R1, R2and R3, according to their
resistive values. The circuit current (I)
flows into/out of thebattery.
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Examples of parallel circuits
Ladder analogy
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Circuit Analysis - Parallel
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DC Circuit Analysis – Parallel
Equivalent resistance
• 1/RT = 1/R1 + 1/R2 + 1/R3
Voltage is the same across all n resistors(V)
Current in each resistor (In)
• In = V/Rn
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DC Circuit Analysis – Parallel
Practice
Analyze a parallel
circuit by finding:
• Equivalent resistance
(RT)
• Circuit current (I)
• Current (In) through each
of the resistors Rn
• I1 through R1
• I2 through R2
• I3 through R3
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Circuit Analysis - Combo
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DC Circuit Analysis – Combo
Resistors are connectedin both series (R3) andparallel (R1, R2) methods
Analyze by starting to
simplify from the inside-out:• Simplify R1 and R2 > R12
• Add result (R12) to R3 for total circuit resistance(Rtot)
Calculate circuit current• I = V/Rtot
Calculate currents throughselected resistances
Shor tcut : Rtot = R3 + 1/(1/R1 + 1/R2)
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Parallel part of combo
Consider current (I)
• Passes through R3
in series with battery• Splits so that larger
part goes through the
low value resistor
(Rlow) , and smaller part goes through
high value (Rhigh)
resistor
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DC Circuit Analysis – Combo
Practice
Given V = 12V, R1,
R2 and R3 = 1, 2, 3
ohm respectively,calculate:
• Equiv resistance (RT)
• Circuit current (I)
• Current through R2 (I2)
• See next slide
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Combo Shortcut for current
R1 and R2 are in parallel, so the voltage
drop across each resistor is the same.
Shortcut for calculating In when there are2 resistors (Rlow and Rhigh) in parallel:
• Ilow = (Rhigh/(Rlow + Rhigh) * circuit current (I)
• Ihigh = (Rlow/(Rlow + Rhigh) * circuit current (I)
We are simply apportioning the current
according to the resistance
• Higher resistance = lower current (and v.v)
Ilow = current through Rlow & Ihigh = current through Rhigh