Kirchhoff’s Rules

Kirchoff’s Rules: Junction Rule• The algebraic sum of the currents into any junction is zero.

• A junction is an intersection of three or more conductors.

Kirchoff’s Rules: Junction Rule

• The algebraic sum of the currents into any junction is zero.

• I = 0 ( at any junction )• I is + when it enters a junction.• I is - when it enters a junction.

• I1 + I2 - I3 = 0

• I = 0

I3

• I1 + I2 = I3

Kirchoff’s Rules: Loop Rule

• The algebraic sum of the potential differences or voltages in any loop, including those associated with emfs and those of resistive elements, must equal zero.

• 3 loops

• V = 0 ( at any loop)

• A loop is any closed conducting path.

Kirchoff’s Rules: Loop Rule

• electron flow

+V

-V:

• Sign convention for V:

Examples:

1. The circuit shown contains two batteries, each with a voltage and an internal resistance, and two resistors. Find: (a) the current in the circuit and (b) the potential difference Vab.

+

-II

-+I

-

+

I

- +I

Examples:

2. In the circuit shown, find: (a) the current in resistor R; (b) the resistance R; (c) the unknown voltage V and (d) if the circuit is broken at point x, what is the current in resistor R? (Ans. (a)2.00 A, (b) 5.00 , (c) 42.0 V, (d) 3.5 A )

V=?

a b

3. Find the voltages V1 and V2 in the circuit below and find the potential difference of point b relative to a. (Ans. V1=18.0 V, V2=7.00 V, Vba=-13.0V.)

Examples:

V1=?

V2=?

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