Electric Circuits

Power Sources Power supplies provide both voltage and current. Direct Current (DC) –Batteries and AC adapters Alternating Current (AC) –Current follows a sine wave. –Ex. Wall outlet

Battery A source of electric potential due to a chemical reaction. Carbon Rod 2e  Zinc Container Zn 2+ NH 4 ClMnO 2 At the Anode At the Cathode

Power Supply Any source of electrical power. It supplies both voltage and current  - Electromotive force r - Internal resistance R - Load resistance  r R Power Supply

Voltage to Load The voltage supplied to a load is given by Ex. What is the voltage supplied by a 9 volt battery, which has an internal resistance of 15 , when a circuit is drawing 250 mA of current?

Resistor Combos Series - The same current goes through each of the resistors. Parallel - The same voltage is applied across each of the resistors. A B R1R1 R2R2 R3R3 AB R1R1 R2R2 R3R3

Kirchoff’s Rules 1Sum of the currents entering a junction equals the sum of the currents leaving a junction. 2Sum of the changes in potential across all the elements in a closed loop is zero.

Loop Traversal Voltage across a resistor –Across a resistor with the current,  I·R –Across a resistor against the current, +I·R Voltage across a power source –Across an emf source from  to +, +  –Across an emf source from + to , 

Network Circuit R 1 =10  R 2 =6  R 3 =8  I1I1 I3I3 I2I2 20V=V a 15V=V b +  +  +  +  +  Node Equation: Loop Equation: I 1 +I 3 =I 2 V a  I 1 R 1 +I 3 R 3 =0 V b  I 3 R 3  I 2 R 2 =0 I 1 +I 3 =I 2 20  I 1 +8I 3 =0 15  I 3  I 2 =0

Bridge Circuit R 3 =12  I1I1 R 1 =15  R 2 =10  R 4 =12  R 5 =5  I5I5 I4I4 I3I3 I2I2 V a =25V IaIa I 1 =I 2 +I 5 I 3 +I 5 =I 4 I 2 +I 4 =I a +25  15I 1  10I 2 =0  15I 1  5I 5 +12I 3 =0  10I 2  5I 5  12I 4 =0

RC Circuits At t = 0s close a switch on an RC circuit with an uncharged capacitor. R C  I Max. Current Max. Charge

Time Constant Charging Capacitor Time Constant, t 0  0.5Q 1.0Q Capacitor Charge Ex. What is the time constant for an RC circuit with R=1.0k  and C=500  F?

Discharging Capacitor At t = 0s the capacitor is discharged through resistor R. I R C +  0  0.5Q 1.0Q Capacitor Charge