Kirchhoffs Law Kirchoff Laws Kirchhoffs Laws apply the

Kirchhoff’s Law

Kirchoff Laws Kirchhoff's Laws apply the Law of Conservation of Energy and the Law of Conservation of Charge. Kirchhoff's Laws deal with current and voltage in electrical connections. There are two basic types of connections (circuits). 1. Series Circuit • electrons flow along one path only:

2. Parallel Circuit • electrons flow along more than one pathway(i. e. alternate branches for current to follow. The total current It will split into branch 1 - I 1 and branch 2 - I 2):

Kirchhoff's Current Law states…. • At any junction in an electric circuit, the total current flowing into the junction is the same as the total current leaving the junction.

• for a series circuit the current at all points will be the same since electrons can flow along only one path. • It= I 1=I 2=I 3=…….

• For a parallel circuit the total current flowing into a connection must equal the sum of the currents flowing out of the connection. • It=I 1+I 2+I 3+……….

Kirchhoff’s Voltage Law states • The algebraic sum of the potential difference (V) around any closed path or loop must be zero.

Series • For a series connection the total potential difference is equal to the sum of the potential differences across each component. • Vt = V 1 + V 2 + V 3+. . +Vn

Parallel • For parallel connections the drop in potential difference across all branches are equal. • Vt = V 1 = V 2 = V 3=. . Vn

Series Parallel Current same add Potential Difference (voltage) add same

Recall: Resistance in circuits • Resistance in a series circuit: – Rt=R 1+R 2+R 3+. . . . • Resistance in parallel circuit: – 1/Rt= 1/R 1+1/R 2+1/R 3

Series Parallel Current same add Potential Difference (voltage) add same Resistance add Add the reciprocal

Series + Parallel • Kirchhoff's Laws can also be applied to a circuit which is a combination of a series and a parallel connection. For example: • Find I 1, I 3, R 1, R 2, R 3, V 1, and V 2

Combined Circuits • Some circuits consist of both series and parallel • To solve these you must find totals for each parallel circuit and then treat the entire circuit as a series circuit

Example

Example

• Find I 1, I 3, R 1, R 2, R 3, V 1, and V 2

Solution • R 1 is in series with the loop and therefore the current passing through R 1 is the same amount entering the loop It= I 1 = 620 m. A. • We don't yet know V 1 so we can not calculate R 1. • 620 m. A enters the parallel connection, 220 m. A travels along one path through R 2. 620 m. A - 220 m. A = 400 m. A travels along the other path through R 3. Therefore I 3 = 400 m. A • We know the current passing through R 3 and the voltage drop across it, now we can calcuate the resistance. R 3 = V 3 / I 3 R 3 = 1. 9 V / 0. 400 A R 2 = 4. 75. • Since the potential difference across the parallel connection is 1. 9 V, V 2 = 1. 9 V. • We know the voltage drop accross R 2 and the current passing through it, now we can calcuate the resistance. R 2 = V 2 / I 2 R 2 = 1. 9 V / 0. 220 A R 2 = 8. 64.

• Practice problems