INC 111 Basic Circuit Analysis Week 2 Kirchoffs

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. ” I 1 I 2 I 3 I 4 I 1 - I 2 - I 3 + I 4 = 0 -I 1 + I 2 + I 3 - I 4 = 0 or

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. ” + V 2 - + + V 1 V 3 - - V 1 – V 2 – V 3 = 0 or -V 1 + V 2 + V 3 = 0

KVL Metaphor C 2 m 5 m B 3 m A

4 V A +2 6 V B Black = voltage compared to the ground -7 +2 2 V -1 V C Close loop +3 D A–B–C–D–A +2 -7 +3 +2 = 0 Red = Voltage difference between 2 points

How to use KVL Form a loop in the circuit

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

Example: Voltage Divider 1 m. A 10 V 4 V 0 V 0 V

R in series Equivalent X m. A

Resistor Reduction Series (อนกรม ) Parallel (ขนาน) or

Example 10 V 7. 5 m. A 10 V 2. 5 m. A 0 V 0 V 0 V

R in parallel Equivalent

Voltage & Current Sources Combination

Example: Current Divider 1. 333 V 1 m. A 1. 333 V 0. 333 m. A 0. 667 m. A 0 V 0 V 0 V

Voltage Divider

Current Divider

Example Find V 1

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

Voltmeter V

Ammeter A

Voltmeter and Ammeter Resistance Characteristic V 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 I 1

KVL on the outer loop