Formula Sheet

Series Circuit:

Total Resistance ­ RT = R1 + R2 + R3 + RN

Total Current ­ IT = ES / RT

Voltage drop ­ V = I x R KVL ­ 0 = ­ ES + VR1 + VR2 + VR3 + .. VRN

Voltage Divider Rule ­ VX = (RX / RT) x E Total Power ­ P = E x I

Parallel Circuit:

Total Current ­ IT = I1 + I2 + I3 + IN or IT = V/RT = Ix.Rx/ RT

Total Resistance ­ RT = 1/(1/R1 + 1/R2 + 1/R3 + .. 1/RN) RT = E / IT Total Resistance for two resistors in parallel ­ RT = (R1 x R2) / (R1 + R2) KCL ­ IT = I1 + I2 + I3 + IN Current Divider Rule ­ Ix = (RT / RX) x IT Special Case for two resistors:

I2 = (R1/R1 + R2) x IT I1 = (R2/R1 +R2) x IT

Total Power ­ PT = P1 + P2 + ... PN

Thevenin to Nortons Conversions: RN = RTH

ETH = RN x IN IN = ETH / RN

Maximum powerPL attains its maximum value when RL = RTH

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Steps to follow for the “Mesh Current” method of analysis:1. Draw mesh currents in loops of circuit, enough to account for all components.2. Label resistor voltage drop polarities based on assumed directions of mesh currents.3. Write KVL equations for each loop of the circuit, substituting the product IR for E in each resistor

term of the equation. Where two mesh currents intersect through a component, express thecurrent as the algebraic sum of those two mesh currents (i.e. I 1 + I 2 ) if the currents go in thesame direction through that component. If not, express the current as the difference (i.e. I 1 ­ I 2).

4. Solve for unknown mesh currents (simultaneous equations).5. If any solution is negative, then the assumed current direction is wrong!6. Algebraically add mesh currents to find current in components sharing multiple mesh currents.7. Solve for voltage drops across all resistors (E=IR).

Superposition Theorem

The Superposition Theorem states that a circuit can be analyzed with only one source of powerat a time, the corresponding component voltages and currents algebraically added to find outwhat they’ll do with all power sources in effect.

To negate all but one power source for analysis, replace any source of voltage (batteries) with awire; replace any current source with an open (break).

Thevenin’s Theorem

Thevenin’s Theorem is a way to reduce a network to an equivalent circuit composed of asingle voltage source, series resistance, and series load. Steps to follow for Thevenin’s Theorem:

1. Find the Thevenin source voltage by removing the load resistor from the original circuit andcalculating voltage across the open connection points where the load resistor used to be.

2. Find the Thevenin resistance by removing all power sources in the original circuit (voltagesources shorted and current sources open) and calculating total resistance between the openconnection points.

3. Draw the Thevenin equivalent circuit, with the Thevenin voltage source in series with theThevenin resistance. The load resistor re­attaches between the two open points of the equivalentcircuit.

4. Analyze voltage and current for the load resistor following the rules for series circuits.

Thevenin to Norton Conversion

Thevenin and Norton resistances are equal. Thevenin voltage is equal to Norton current times Norton resistance. Norton current is equal to Thevenin voltage divided by Thevenin resistance.

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