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Circuit Analysis with E quivalent 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 ) = 5 Ω + 6 Ω + 9 Ω

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Circuit analysis with e quivalent resistance
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
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
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
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
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
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
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 a cross parallel components
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
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
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
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