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Comprehensive Guide to Circuit Analysis Using Equivalent Resistance

This guide walks you through the essential techniques of circuit analysis focused on equivalent resistance. It details the step-by-step process of simplifying complex circuits by combining series and parallel resistors. Starting from simple configurations, we methodically combine resistors to reach a final equivalent resistance. The application of Ohm's Law is emphasized throughout to compute voltages and currents across individual resistors after simplification. This resource is ideal for electrical engineering students and enthusiasts seeking to deepen their understanding of circuit behavior.

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Comprehensive Guide to Circuit Analysis Using Equivalent Resistance

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  1. 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

  2. Combine the Series Resistors Series resistors R(equiv) = R1 + R2 + R3 R(equiv) = 5Ω + 6Ω + 9Ω R(equiv) = 20Ω R1 R2 R3 Req

  3. 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

  4. More Series Combination R1 Series resistors R(equiv) = R1 + R2 + R3 R(equiv) = 2Ω+ 4Ω+ 8Ω R(equiv) = 14Ω R2 R3 Req

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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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