INC 112 Basic Circuit Analysis Week 2 Kirchhoff's laws

Kirchoff’s Current Law (KCL) “The sum of all currents entering a point is equal zero.” I1 I4 I3 I2 I1 - I2 - I3 + I4 = 0or -I1 + I2 + I3 - I4 = 0

KCL Metaphor From the pipe that is full of water, the amount of flow-in water must be equal to the amount of flow- out water. This is because water cannot disappear.

How to use KCL Place a circle anywhere any size that you want

Kirchoff’s Voltage Law “The sum of all voltages in a closed loop is equal zero.” + V1 - + V3 - +V2- V1 – V2 – V3 = 0or-V1 + V2 + V3 = 0

KVL Metaphor 2 m 3 m 5 m A C B

How to use KVL Form a loop in the circuit

Example: Voltage Divider X mA KCL: Current is the same at all points in all the circuit because there is no branch. KVL:

Voltage Divider Circuit 1mA 0V 10V 4V 0V

Resistor Reduction Series Parallel or

Example 7.5mA 0V 10V 0V 10V 0V 2.5mA 5mA

Voltage & Current Sources Combination

Example: Current Divider 1mA 0V 1.333V 0V 1.333V 0V 0.333mA 0.667mA

Voltage Divider

Current Divider

Example Find V1

Circuits with more than 1 ground Same circuit

Voltmeter and Ammeter V Voltmeter: Measure the voltage between 2 points Usage: Put each pin on each point A Ammeter: Measure the current that passes through a wire Usage: Cut that wire and connect the cut to the ammeter

Voltmeter V

Ammeter A

Voltmeter and Ammeter V Same as electric wire Property: R = 0 ohm A Same as open circuit Property: Very high resistance

Dependent Source The amount of voltage (current) supplied depends on other voltage (current). Dependent Voltage Source Dependent Current Source

Example Find I