Kirchoff’s Rules. tml.

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Presentation transcript:

Kirchoff’s Rules

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Junction: a point where at least three branches meet. Branch: a path connecting two junctions.

Junction Rule: ΣI in = ΣI out The sum of the current going into a junction is equal to the sum of the current flowing out of a junction. Loop Rule: ΣV = 0 The total voltage of the circuit is equal to 0.

Steps for solving for current using Kirchoff’s rules 1.Use the junction rule to write an equation for the currents in the circuit. 2.Use the loop rule and write equations for each loop. Use your finger to trace a path around the loop and be sure to end where you began. 3.Plug in what you know, to your loop equations. 4.Using the equation found by the junction rule, rearrange it so that you can substitute this equation in for one of your currents. 5.Simplify your equations. 6.Using a system of equations, one current variable should drop out and you will be left with one current variable you can solve for. 7.Use the value from step 6 to solve for the other two currents by plugging it in to the other equations.

Example: Using Kirchoff’s rules, find the current in each branch. R 1 = 6 Ω R 2 = 4 Ω R 3 = 4 Ω R 4 = 1 Ω Ε1 = 30 V E2 = 12 V E3 = 6 V

Using the loop rule we get: left loop: E 1 –I 1 R 1 -I 3 R 4 -E 3 =0 right loop: E 3 +I 3 R 4 -I 2 R 3 -E 2 =0 Using the junction rule we get: I 1 = I 2 + I 3

Use the equations on the following slide, solve for I 1, I 2, I 3.

Power

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