Ohm’s Law “Current (I) is proportional to Voltage (V) and inversely proportional to Resistance (R)”

Resistance uses power from the source. Power in electronics is measured in Watts. In addition to the value in ohms, resistors are also rated according to their ability to dissipate power.

Kirchhoff’s Voltage Law Used in series circuits Current is the same “The sum of the voltage drops equals the applied voltage”

Series Circuits One current path, therefore the current is the same everywhere Total resistance is the sum of the individual resistances

Across AB the voltage is : 12 x ½ = 6V and the same for BC. Across AB is half of the total resistance. The voltage drops by a half across AB and then another half across BC. Series Circuits

R1 is 1/6th of the total resistance and the voltage at R1 is 2V R2 is 2/6th of the total resistance and the voltage at R2 is 4V R3 is 3/6th of the total resistance and the voltage at R3 is 6V As the resistance increases the drop in the voltage increases. Series Circuits

Now, how much power is dissipated by R1? P = I 2 x R1 = (.002)2A x 1000 O =.004W = 4mW And for the whole circuit? Simply add the resistances. Pt = Vt x I =12A x.002 O =.0024W =24mW Series Circuits

If resistors don’t do anything but produce heat, then why do we need them? Because resistors are also used: to divide a voltage and deliver different voltages to different devices to limit the amount of current being delivered to other devices. to discharge a voltage stored in some components when the power is turned off.

Kirchhoff’s Current Law Use in parallel circuits. “The current entering a junction must equal the current leaving the junction”

Parallel Circuits Voltage is the same More than one current path Total current is the sum of the individual currents

The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total: equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R Parallel Circuits

If the values of the three resistors are: R1 = 8 O, R2 = 8 O, R3 = 4 O The total resistance is found by: 1/R = 1/8 + 1/8 + ¼ = ½ This gives R = 2 Ohms With a 10 V battery, using V = I R The total current in the circuit is: I = V / R = 10 / 2 = 5 A. The individual currents can also be found using Ix = V / Rx. The voltage across each resistor is 10 V, so: I 1 = 10 / 8 = 1.25 A I 2 = 10 / 8 = 1.25 A I 3 =10 / 4 = 2.5 A Note that the currents add together to 5A, the total current. Parallel Circuits

When calculating the equivalent resistance (Re) in a set of parallel resistors, don’t forget to flip the 1/R upside down. To check your answer the equivalent resistance will always be Smallest resistance < equivalent resistance < smallest resistance Number of resistors Three resistors in parallel: 6 ohms, 9 ohms, and 18 ohms. The smallest resistance is 6 ohms and 6/3 = 2 ohms. Re = 1/6 + 1/12 + 1/18 = 6/18. Flipping this upside down gives 18/6 = 3 ohms, which is certainly between 2 and 6.

Parallel Circuits If the resistors in parallel are identical: The equivalent resistance of N identical resistors The resistance of one resistor divided by N, the number of resistors. = The equivalent resistance of two 40-ohm resistors The resistance of 40-ohm divided by 2, the number of resistors. Which is 20-ohm = The equivalent resistance of five 50-ohm resistors The resistance of 50-ohm divided by 5, the number of resistors. Which is 10-ohm =

Series AND Parallel Circuits The total resistance in a circuit with resistors in a combination of both series and parallel is found by reducing the different series and parallel combinations step-by-step to end up with a single equivalent resistance for the circuit. This allows the current to be determined easily. The current flowing through each resistor can then be found by undoing the reduction process.

Series AND Parallel Circuits General rules for doing the reduction process include: Two (or more) resistors in parallel can be reduced to one resistor using the equivalent resistance equation for resistors in parallel. Two (or more) resistors connected in series can be reduced to one equivalent resistor. Finally, remember that for resistors in series, the current is the same for each resistor, and for resistors in parallel, the voltage is the same for each one.