1. Parallel Circuit

2. Same Voltage  Two circuit elements joined together at both ends are in parallel. Multi-wire connectionMulti-wire connection  The potential is the same across each element.  The two elements have the same voltage. May have different currentMay have different current

3. Junctions  The place where wires join is called a junction. Three wires at a point  Charges flow into and out of the junction. Remains neutral  A voltmeter measures across an element. No current through voltmeter I2I2 I1I1 I3I3 R I V V I I

4. Kirchhoff’s Current Law  Electrons flowing into and out of a junction do not stop. Charge remains neutral – no build up or deficitCharge remains neutral – no build up or deficit  The total current at each junction must be zero. Sum of currents must be zeroSum of currents must be zero Conservation of chargeConservation of charge  This is Kirchhoff’s current law.

5. Parallel Resistors  Resistors can be joined in parallel. Both ends connected  Ohm’s law gives the current through each resistor. Sum for total current Factor out voltage  The inverse of the resistance is the sum of the individual inverse resistances. R1R1 R2R2 R3R3 I V

6. Networks 5 k   Find the equivalent resistance of the pictured set of resistors.  This can be separated into two problems. The parallel 2 k  and 3 k  resistorsThe parallel 2 k  and 3 k  resistors The series 5 k  resistorThe series 5 k  resistor  The equivalent resistance is 6.2 k . 2 k  3 k  5 k  6/5 k 

7. Parallel Batteries?  Equal batteries can be placed in parallel. Voltage the sameVoltage the same Additional current availableAdditional current available Additional powerAdditional power  Unequal batteries should usually not be placed in parallel. Excess voltage drains batteryExcess voltage drains battery Short circuitShort circuit OK for battery chargerOK for battery charger 9 V 1.5 V9 V I I

8. Branch Analysis  Find the current in the 5 k  resistor in the circuit at left. V 1 = 16 V V 2 = 6 V R 1 = 2 k  R 2 = 4 k  R 3 = 5 k   Assign a current to each branch. Unknown currents Direction arbitrary R1R1 R2R2 R3R3 V1V1 V2V2 I1I1 I2I2 I3I3

9. Kirchhoff Applied R1R1 R2R2 R3R3 V1V1 V2V2 I1I1 I2I2 I3I3 Voltage law (2 loops) Current law Three equations, three unknowns

10. Unknown Current  The equation can be solved for the current I 3. Substitute values  I 3 = 2 mA next R1R1 R2R2 R3R3 V1V1 V2V2 I1I1 I2I2 I3I3