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:
 RT = R1+ R2+ R3 ...+ etc.
 Where RT is the total resistance and R1,
R2, R3 are individual series resistances.
I = ET / RT
 RT is the sum of all resistances.
 ET 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.
 V1, V2 etc are used for the voltage drops
across each resistor to distinguish them from
the applied voltage source ET. V1 = IT X R1,
V2 = IT X R2, etc
 ET = 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 ET
 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:
 PT = P1 + P2 + ...+ etc
 Remember: 3 Power Formulas
 P=ExI
 P = I2 x R
 P = E2 / 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
R1 = 2Ω R2 = 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
 I1 = E / R1
 I2 = E / R2 and so on.
 If individual resistances are the same, then
individual branch currents would also be
the same.
Main-line IT = sum of branch
currents
 IT = I1 + I2 + ...+ 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.
 RT = E / IT
 RT is always less than the smallest
individual branch resistance
Reciprocal resistance
formulae
 1 / RT = 1/R1 + 1/R2 + 1/R3 + ... 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:
 R1 x R2/R1 + R2 = Total resistance
Finding an unknown R
 In able to find what value Rx must be
added in parallel with a known R to get a
required Rt
 R x RT/R - RT = Rx
Power in parallel circuits
 Total power equals the sum of the
individual power in each branch.
 PT = P1 + P2 + ...+ 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.
 I1 =R2/R1 + R2 (IT)
 I2 =R1/R1 + R2 (IT)
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