CALCULATIONS FOR CIRCUITS SELECTING
BETWEEN SERIES OR PARALLEL OPERATION
OF VARIOUS ELECTRICAL DEVICES

Calculations for series and parallel circuits of loads

Here are the formulas for calculation of the parameters of series and parallel circuits of lamps, speakers, or impedances.

The rows marked "SAME" have identical impedances for all of the lamps, speakers, or impedance items in the circuit.

The rows marked "DIFF" do not have identical impedances for all of the lamp or impedance items in the circuit.

 
Light Bulbs, Speakers, and Impedances
 
TYPE Parameter Number n Resistance R Current I Voltage V Power P
  Ri Original (o) Values n = 1 Ro = Vo / Io Io = Po / Vo Vo = Rated V Po = Rated W
 
S
E
R
I
E
S
D
I
F
F
Totals n = # Lamps Rt = Σ(Ri, i=1,n) It = Vt / Rt Vt = Vs (Supply) Pt = Vt × It
Individual n = # Lamps Ri = Vt / It Ii = It Vi = It × Ri Pi = Vi × Ii
Ri = Vi 2 / Pi Ii = Vt / Rt Vi = Pi / It Pi = Vi 2 / Ri
 
S
A
M
E
Totals (Vs = Vo) n = # Lamps Rt = Ro × n It = Io / n Vt = Vo Pt = Po / n
Individual (Vs = Vo) n = # Lamps Ri = Ro Ii = Io / n Vi = Vo / n Pi = Po / n 2
Total (Vs ≠ Vo) n = # Lamps Rt = Ro × n It = Vs / Rt Vt = Vs Pt = Vs 2 / Rt
Individual (Vs ≠ Vo) n = # Lamps Ri = Ro Ii = Vs / Rt Vi = Vs / n Pi = Pt / n 2
 
P
A
R
A
L
L
E
L
D
I
F
F
Totals n = # Lamps Rt = 1 / Σ(1 / Ri, i=1,n) It = Vt / Rt Vt = Vs (Supply) Pt = Vt × It
Individual n = # Lamps Ri = Vs / Ii Ii = Pi / Vs Vi = Vs Pi = Vs × Ii
Ri = Vs 2 / Pi Ii = Vs / Ri Vi = Vt Pi = Vs 2 / Ri
 
S
A
M
E
Totals (Vs = Vo) n = # Lamps Rt = Ro / n It = Io × n Vt = Vo Pt = Po × n
Individual (Vs = Vo) n = # Lamps Ri = Ro Ii = Io Vi = Vo Pi = Po
Total (Vs < Vo) n = # Lamps Rt = Ro / n It = Vs / Rt Vt = Vs Pt = Vs 2 / Rt
Individual (Vs ≠ Vo) n = # Lamps Ri = Ro Ii = Vs / Ri Vi = Vs Pi = Pt / n
 
P
A
R

S
E
R
S
A
M
E
Totals (Vs = Vo) n 2 = # Lamps
n = # Lamps / Series
n = # of Series
Rt = Ro It = Io Vt = Vo Pt = Po
Individual (Vs = Vo) Ri = Ro Ii = Io / n Vi = Vo / n Pi = Po / n 2
Total (Vs < Vo) n 2 = # Lamps
n = # Lamps / Series
n = # of Series
Rt = Ro It = Vs / Ro Vt = Vs Pt = Vs 2 / Ro
Individual (Vs ≠ Vo) Ri = Ro Ii = Vs / Ro / n Vi = Vs / n Pi = Pt / n 2
 

Calculations for series and parallel circuits of batteries

Here are the formulas for calculation of the parameters of series and parallel circuits of batteries.

The rows marked "SAME" have identical characteristics for all of the batteries in the circuit.

Use of batteries with different characteristics causes problems with battery life.

 
Batteries
 
TYPE Parameter Number n Current Imax Current Iτ Voltage V Energy ε
Cells Original (o) Values n = 1 Io = Rated Imax o = Rated A Hr Vo = Rated V εo = Rated W Hr
 
S
E
R
I
E
S
S
A
M
E
Totals
 
 
n = # Cells It = Io t = Iτo Vt = Vo × n εt = εo × n
Individual
Cells
 
n = # Cells Ii = Io i = Iτo Vi = Vo εi = εo
 
P
A
R
A
L
L
E
L
S
A
M
E
Totals
 
 
n = # Cells It = Io × n t = Iτo × n Vt = Vo εt = εo × n
Individual
Cells
 
n = # Cells Ii = Io i = Iτo Vi = Vo εi = εo
 
P
A
R

S
E
R
S
A
M
E
Totals
 
 
n 2 = # Cells
n = # Cells / Series
n = # of Series
It = Io × n t = Iτo × n Vt = Vo × n εt = εo × n 2
Individual
Cells
 
Ri = Ro Ii = Io Vi = Vo εi = εo
 

LINKS

LINKS:

  1. CIRCUITS SELECTING SERIES OR PARALLEL OPERATION
  2. LIGHT BULBS, SPECTRA, and HUMAN VISION
  3. Computers, Science, and Measurement