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• Kirchoff’s Voltage Law: “The sum of all voltages about a closed loop in a circuit is equal to zero” - Each element will have a voltage (potential) between nodes. If any two points on the closed loop are chosen, and different paths chosen between them, the potentials must be equal or current will flow in a loop indefinately (Note: this would be perpetual motion).
3.1.1 Simple Applications of Kirchoff’s Laws
3.1.1.1 - Parallel Resistors
• Let’s consider one on the most common electrical calculations - that for resistors in parallel. We want to find the equivalent resistance for the network of resistors shown.
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First we can define cur- |
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Now, consider the sum of the currents in and out of the upper conductor,
∑ I = I – I1 – I2 – … – In = 0
The current through each resistor is simple to calculate, so if we add the current through the resistors, and then relate the expression to Rp, the equation becomes,
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3.1.1.2 - Series Resistors
• Now consider another problem with series resistors. We can use Kirchoff’s voltage law to sum the voltages in the circuit loop. In this case the input voltage is a voltage rise, and the resistors are voltage drops (the signs will be opposite).