INC 111 Basic Circuit Analysis Week 2 Kirchoff’s Law

Kirchoff’s Current Law (KCL) “The sum of all currents entering a point is equal zero.” I1 I2 I3 I4 I1 - I2 - I3 + I4 = 0 or -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.” + V2 - + V1 - + V3 - V1 – V2 – V3 = 0 or -V1 + V2 + V3 = 0

KVL Metaphor C 2 m 5 m B 3 m A

How to use KVL Form a loop in the circuit

Example: Voltage Divider X mA KCL: Current is equal on all points in the circuit because there is no separate path KVL:

Example: Voltage Divider 1mA 0V 10V 4V

R in series Equivalent X mA X mA

Resistor Reduction Series (อนุกรม) Parallel (ขนาน) or

Example 7.5mA 0V 10V 2.5mA 5mA

R in parallel Equivalent

Voltage & Current Sources Combination

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

Voltage Divider

Current Divider

Example Find V1

Voltmeter and Ammeter Voltmeter measures the difference of voltage between 2 points. Put 2 connectors to 2 points that we want to know the voltage difference. V Ammeter measures the current pass through wire. Cut the wire, and put the two open-ends to the meter. A

Voltmeter V

Ammeter A

Voltmeter and Ammeter Resistance Characteristic Same as open circuit ( not connected) A Same as conductor (wire)

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

Example Find I

Example Find I1

KVL on the outer loop