# 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 n = 1 Ro = Vo / Io Io = Po / Vo Vo = Rated V Po = Rated W n = # Lamps Rt = Σ(Ri, i=1,n) It = Vt / Rt Vt = Vs (Supply) Pt = Vt × It 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 n = # Lamps Rt = Ro × n It = Io / n Vt = Vo Pt = Po / n n = # Lamps Ri = Ro Ii = Io / n Vi = Vo / n Pi = Po / n 2 n = # Lamps Rt = Ro × n It = Vs / Rt Vt = Vs Pt = Vs 2 / Rt n = # Lamps Ri = Ro Ii = Vs / Rt Vi = Vs / n Pi = Pt / n 2 n = # Lamps Rt = 1 / Σ(1 / Ri, i=1,n) It = Vt / Rt Vt = Vs (Supply) Pt = Vt × It 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 n = # Lamps Rt = Ro / n It = Io × n Vt = Vo Pt = Po × n n = # Lamps Ri = Ro Ii = Io Vi = Vo Pi = Po n = # Lamps Rt = Ro / n It = Vs / Rt Vt = Vs Pt = Vs 2 / Rt n = # Lamps Ri = Ro Ii = Vs / Ri Vi = Vs Pi = Pt / n n 2 = # Lamps n = # Lamps / Seriesn = # of Series Rt = Ro It = Io Vt = Vo Pt = Po Ri = Ro Ii = Io / n Vi = Vo / n Pi = Po / n 2 n 2 = # Lamps n = # Lamps / Seriesn = # of Series Rt = Ro It = Vs / Ro Vt = Vs Pt = Vs 2 / Ro 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 n = 1 Io = Rated Imax Iτo = Rated A Hr Vo = Rated V εo = Rated W Hr n = # Cells It = Io Iτt = Iτo Vt = Vo × n εt = εo × n n = # Cells Ii = Io Iτi = Iτo Vi = Vo εi = εo n = # Cells It = Io × n Iτt = Iτo × n Vt = Vo εt = εo × n n = # Cells Ii = Io Iτi = Iτo Vi = Vo εi = εo n 2 = # Cells n = # Cells / Seriesn = # of Series It = Io × n Iτt = Iτo × n Vt = Vo × n εt = εo × n 2 Ri = Ro Ii = Io Vi = Vo εi = εo