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Circuit Analysis with E quivalent ResistancePowerPoint Presentation

Circuit Analysis with E quivalent Resistance

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Circuit Analysis with Equivalent Resistance

To solve this circuit we must simplify

Start from the right and work to the left

Each combination opens new options

Combine the Series Resistors

Series resistors

R(equiv) = R1 + R2 + R3

R(equiv) = 5Ω + 6Ω + 9Ω

R(equiv) = 20Ω

R1

R2

R3

Req

Combine the Parallel Resistors

Now the 5 Ohm and 20 Ohm resistors are in a parallel configuration.

R(equiv) = 1/((1/R1)+(1/R2))

R(equiv) = 1/((1/5) + (1/20))

R(equiv) = 1/((4/20)+(1/20))

R(equiv) = 1/(5/20)

R(equiv) = 4Ω

R2

R1

Req

More Series Combination

R1

Series resistors

R(equiv) = R1 + R2 + R3

R(equiv) = 2Ω+ 4Ω+ 8Ω

R(equiv) = 14Ω

R2

R3

Req

More Parallel Combination

Now the 14 Ohm and 4 Ohm resistors are in a parallel configuration.

R(equiv) = 1/((1/R1)+(1/R2))

R(equiv) = 1/((1/4) + (1/14))

R(equiv) = 1/((14/56)+(4/56))

R(equiv) = 1/(18/56)

R(equiv) = 3.11Ω

R1

R2

Req

Final Series Combination

R1

A final series combination completes the circuit simplification

Series resistors

R(equiv) = R1 + R2 + R3

R(equiv) = 1Ω+ 3.11Ω+ 7Ω

R(equiv) = 11.11Ω

R2

R3

Req

Work back to find all voltages and currents to solve circuit

Total current through circuit

V/R = I

In a series circuit, the current is the same through each resistor

Sum of voltage drops is equal to the voltage drop across equivalent resistor

Use Ohms law to find the voltage drop across each resistor

V = IR for each resistor

Example with 24 V applied across

A and B

Same Voltage Across Parallel Components

Voltage drop across the equivalent resistor is the voltage drop across each of the resistors

Sum of the currents is equal to the current through the equivalent resistor

Current Divided

Use Ohms Law to get the current across each of the resistors

I = V/R for each resistor

Voltage from previous

Series Resistors Divide Voltage

In a series circuit, the current is the same through each resistor

Sum of voltage drops is equal to the voltage drop across equivalent resistor

Use Ohms law to find the voltage drop across each resistor

V = IR for each resistor

Current from previous

Parallel Resistors Divide Current

Voltage drop across the equivalent resistor is the voltage drop across each of the resistors

Sum of the currents is equal to the current through the equivalent resistor

Use Ohms Law to get the current across each of the resistors

I = V/R for each resistor

Voltage from previous

More Series Voltage Division

In a series circuit, the current is the same through each resistor

Sum of voltage drops is equal to the voltage drop across equivalent resistor

Use Ohms law to find the voltage drop across each resistor

V = IR for each resistor

Current from previous

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