# Physics Assignment Help With Kirchhoff's Laws

## 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.

## 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.

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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