Basic Electronics II Series and Parallel Circuits

Series Circuits  When components are connected in successive order.  Only one path for electron flow.  Current is the same for all series components.

Series Circuits

Total R = sum of all series resistances:  R T = R 1 + R 2 + R 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 + V 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 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.

Parallel Circuits R 1 = 2Ω R 2 = 4Ω

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 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 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 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