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Equivalent Resistance

Equivalent Resistance. Kirchhoff’s Rules. What is Equivalent Resistance?. Equivalent resistance is the resistance needed to replace all individual resistors in a circuit with a single resistor and maintain the same voltage and current.

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Equivalent Resistance

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  1. Equivalent Resistance Kirchhoff’s Rules

  2. What is Equivalent Resistance? • Equivalent resistance is the resistance needed to replace all individual resistors in a circuit with a single resistor and maintain the same voltage and current. • How you find this equivalent resistance depends on the type of circuit you are dealing with

  3. Series Circuit • Total voltage of circuit is equal to the sum of the voltages of the parts VTotal = V1 + V2 +V3 +… • The voltage drop across each MUST equal the total drop of the circuit…like a series of waterfalls…

  4. Series Circuit • Total current of the circuit is constant ITotal = I1 = I2 =I3 =… • If you think of current like a conga line you can see why the current at any given point is the same (demo)…

  5. Series Circuit • Equivalent resistance is equal to the sum of the resistances of the parts Requivalent = R1 + R2 +R3 +… • Electricity will take the path of least resistance, so if there is only one path, the resistances add up as the electricity passes.

  6. VT = 60 V • V1 = 25 V • V2 = ____ • V3 = ____ • REq = ____ • R1 = ____ • R2 = 15 Ω • R3 = ____ • IT = 2 A • I1 = ____ • I2 = ____ • I3 = ____ R1 R2 R3

  7. Parallel Circuit • Total voltage of circuit is constant VTotal = V1 = V2 = V3 =… • There is more than one path, so each resistor (or object in the circuit) is technically connected directly to the batter (or voltage source) so it will have the same Voltage as the source. It’s like dropping things all from the same level…

  8. Parallel Circuit • Total current of the circuit is equal to the sum of the currents of the parts ITotal = I1 + I2 +I3 +… • Like a river, or system of pipes…when the current comes to a fork, it splits. But we cannot create current that didn’t exist before, so the currents must all add up to the total. 5 8 12 12 4 3 1 4 3

  9. Parallel Circuit • Equivalent resistance is equal to the reciprocal of the sum of the reciprocals resistances of the parts (1/REq ) = (1/R1 ) + (1/R2 ) +(1/R3 ) +… • Since there is more than one path, the electricity can find the path of least resistance, so the overall resistance of the circuit is actually less than the sum of the individual resistances.

  10. VT = ____ • V1 = 30 V • V2 = ____ • V3 = ____ • REq = ____ • R1 = ____ • R2 = 15 Ω • R3 = ____ • IT = 18 A • I1 = ____ • I2 = ____ • I3 = 10 A R1 R3 R2

  11. Combined Circuits • Some circuits (actually, most circuits) actually consist of combinations of series and parallel parts. • When dealing with these combination circuits, treat each part as a separate circuit and find the equivalence of that part…then combine the equivalences into one new circuit that is either series or parallel….

  12. R2 • VT = 120 V • V1 = _____ • V2 = ____ • V3 = ____ • V4 = ____ • REq = ____ • R1 = 8 Ω • R2 = 18 Ω • R3 = ____ • R4 = 6 Ω • IT = ____ • I1 = ____ • I2 = ____ • I3 = ____ • I4 = 6 A R1 R3 R4

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