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11.7 Kirchhoff's Laws

The two laws of Kirchoff are based on the conservation of charge and the conservation of energy, respectively.

11.7.1 Kirchhoff's Current Law (KCL)

At any circuit junction the sum of the currents entering the junction must equal the sum of the current leaving the junction.

I1 – I2 + I3 – I4 = 0
or I1 + I3 = I­2 + I4
It is based on conservation of charge. As current flows through various branches of a circuit, nowhere the charges accumulate or disappear.
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11.7.2 Kirchhoff's Voltage Law (KVL)

The sum of voltage changes across all the circuit elements found when traversing one direction around any closed circuit-loop must be zero.

It is based on energy conservation. As charge q moves around a complete circuit loop, its energy gains and losses must total zero.

11.7.3 Application of Kirchhoff's law in a circuit

Assume currents along with their directions in each branch of the complex circuit. After assuming currents in each branch, we pick a point and begin to walk (mentally) around a circuit loop. As we traverse each resistor or battery we must write down the voltage change for that element according to the following four rules.

1. If we traverse through a battery from the negative terminal to the positive terminal, the change in voltage is +E.

2. If we traverse through a battery from the positive terminal to the negative terminal, the change in voltage is -E.
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3. If a resistor is traversed in the same direction as the assumed current flow, the change in potential is -IR

4. If a resistor is traversed in the direction opposite from the assumed current flow, the change in potential is +IR.
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