Total R = sum of all series resistances: R T = R 1 + R 2 + R 3... + etc. Where R T is the total resistance and R 1, R 2, R 3 are individual series resistances.
I = E T / R T R T is the sum of all resistances. E T is the voltage applied across the total resistance. I is the current in all parts of the string.
Series IR Voltage Drops The IR voltage across each resistance is known as an IR drop or a voltage drop. It reduces the potential difference available for the remaining resistance in a series circuit. V 1, V 2 etc are used for the voltage drops across each resistor to distinguish them from the applied voltage source E T. V1 = I T X R 1, V2 = I T X R 2, etc E T = V1 + V2 +.... + etc
Voltage Divider An arrangement of 2 resistors in series is often called a voltage divider. Each IR drop V = its proportional part of the applied voltage or: V = R / R T x E T A potentiometer (volume control) is a voltage divider where the point of division is made variable.
Total Power in Series Circuits The total power is the sum of the power dissipated in each part of the circuit or: P T = P 1 + P 2 +...+ etc Remember: 3 Power Formulas P = E x I P = I 2 x R P = E 2 / R
Effect of an open is a series circuit Because the current is the same in each part of a series circuit - An open results in no current for the entire circuit.
Parallel Circuits Each parallel path is a branch with its own individual current. Parallel circuits have one common voltage across all branches, however - Individual branch currents can be different.
Voltage is equal across parallel branches Since components are directly connected across the voltage source, they must have the same potential as the source. Therefore, the voltage is the same across components connected in parallel. Components requiring the same voltage would be connected in parallel.
Each branch I = E / R I 1 = E / R 1 I 2 = E / R 2 and so on. If individual resistances are the same, then individual branch currents would also be the same.
Main-line I T = sum of branch currents I T = I 1 + I 2 +...+ etc
Resistances in parallel Total resistance across the main line can be found by Ohm’s Law: Divide the common voltage by the total current. R T = E / I T R T is always less than the smallest individual branch resistance
Reciprocal resistance formulae 1 / R T = 1/R 1 + 1/R 2 + 1/R 3 +... etc This formulae works for any number of parallel resistances of any value
If the values of R are the same If all resistors in parallel are the same value, then use this shortcut: The value of one resistor/total number of resistors = Total resistance
If the there are only 2 resistors of differing values If there are only two resistors in parallel and they are different in value, then use this shortcut: R 1 x R 2 /R 1 + R 2 = Total resistance
Finding an unknown R In able to find what value R x must be added in parallel with a known R to get a required R t R x R T /R - R T = R x
Power in parallel circuits Total power equals the sum of the individual power in each branch. P T = P 1 + P 2 +...+ etc In both series and parallel circuits the sum of the individual values of power dissipated in the circuit = the total power generated by the source.
Parallel Current Dividers Individual branch currents can be found without knowing the applied voltage. Currents divide inversely as the branch resistances. I 1 =R 2 /R 1 + R 2 (I T ) I 2 =R 1 /R 1 + R 2 (I T )
Effect of an open in a parallel circuit An open in the main line results in no current in all branches An open in a branch results in no current for that individual branch - other branches are not affected
Effect of a short circuit in parallel A short circuit has practically zero resistance A short results in excessive current