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 | |
R_{i} | Original (o) Values | n = 1 | R_{o} = V_{o} / I_{o} | I_{o} = P_{o} / V_{o} | V_{o} = Rated V | P_{o} = Rated W | |
S E R I E S |
D I F F |
Totals | n = # Lamps | R_{t} = Σ(R_{i}, i=1,n) | I_{t} = V_{t} / R_{t} | V_{t} = V_{s} (Supply) | P_{t} = V_{t} × I_{t} |
Individual | n = # Lamps | R_{i} = V_{t} / I_{t} | I_{i} = I_{t} | V_{i} = I_{t} × R_{i} | P_{i} = V_{i} × I_{i} | ||
R_{i} = V_{i} ^{2} / P_{i} | I_{i} = V_{t} / R_{t} | V_{i} = P_{i} / I_{t} | P_{i} = V_{i} ^{2} / R_{i} | ||||
S A M E |
Totals (V_{s} = V_{o}) | n = # Lamps | R_{t} = R_{o} × n | I_{t} = I_{o} / n | V_{t} = V_{o} | P_{t} = P_{o} / n | |
Individual (V_{s} = V_{o}) | n = # Lamps | R_{i} = R_{o} | I_{i} = I_{o} / n | V_{i} = V_{o} / n | P_{i} = P_{o} / n ^{2} | ||
Total (V_{s} ≠ V_{o}) | n = # Lamps | R_{t} = R_{o} × n | I_{t} = V_{s} / R_{t} | V_{t} = V_{s} | P_{t} = V_{s} ^{2} / R_{t} | ||
Individual (V_{s} ≠ V_{o}) | n = # Lamps | R_{i} = R_{o} | I_{i} = V_{s} / R_{t} | V_{i} = V_{s} / n | P_{i} = P_{t} / n ^{2} | ||
P A R A L L E L |
D I F F |
Totals | n = # Lamps | R_{t} = 1 / Σ(1 / R_{i}, i=1,n) | I_{t} = V_{t} / R_{t} | V_{t} = V_{s} (Supply) | P_{t} = V_{t} × I_{t} |
Individual | n = # Lamps | R_{i} = V_{s} / I_{i} | I_{i} = P_{i} / V_{s} | V_{i} = V_{s} | P_{i} = V_{s} × I_{i} | ||
R_{i} = V_{s} ^{2} / P_{i} | I_{i} = V_{s} / R_{i} | V_{i} = V_{t} | P_{i} = V_{s} ^{2} / R_{i} | ||||
S A M E |
Totals (V_{s} = V_{o}) | n = # Lamps | R_{t} = R_{o} / n | I_{t} = I_{o} × n | V_{t} = V_{o} | P_{t} = P_{o} × n | |
Individual (V_{s} = V_{o}) | n = # Lamps | R_{i} = R_{o} | I_{i} = I_{o} | V_{i} = V_{o} | P_{i} = P_{o} | ||
Total (V_{s} < V_{o}) | n = # Lamps | R_{t} = R_{o} / n | I_{t} = V_{s} / R_{t} | V_{t} = V_{s} | P_{t} = V_{s} ^{2} / R_{t} | ||
Individual (V_{s} ≠ V_{o}) | n = # Lamps | R_{i} = R_{o} | I_{i} = V_{s} / R_{i} | V_{i} = V_{s} | P_{i} = P_{t} / n | ||
P A R − S E R |
S A M E |
Totals (V_{s} = V_{o}) | n ^{2} = # Lamps
n = # Lamps / Series n = # of Series |
R_{t} = R_{o} | I_{t} = I_{o} | V_{t} = V_{o} | P_{t} = P_{o} |
Individual (V_{s} = V_{o}) | R_{i} = R_{o} | I_{i} = I_{o} / n | V_{i} = V_{o} / n | P_{i} = P_{o} / n ^{2} | |||
Total (V_{s} < V_{o}) | n ^{2} = # Lamps
n = # Lamps / Series n = # of Series |
R_{t} = R_{o} | I_{t} = V_{s} / R_{o} | V_{t} = V_{s} | P_{t} = V_{s} ^{2} / R_{o} | ||
Individual (V_{s} ≠ V_{o}) | R_{i} = R_{o} | I_{i} = V_{s} / R_{o} / n | V_{i} = V_{s} / n | P_{i} = P_{t} / n ^{2} | |||
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 I_{max} | Current Iτ | Voltage V | Energy ε | |
Cells | Original (o) Values | n = 1 | I_{o} = Rated I_{max} | Iτ_{o} = Rated A Hr | V_{o} = Rated V | ε_{o} = Rated W Hr | |
S E R I E S |
S A M E |
Totals |
n = # Cells | I_{t} = I_{o} | Iτ_{t} = Iτ_{o} | V_{t} = V_{o} × n | ε_{t} = ε_{o} × n |
Individual Cells |
n = # Cells | I_{i} = I_{o} | Iτ_{i} = Iτ_{o} | V_{i} = V_{o} | ε_{i} = ε_{o} | ||
P A R A L L E L |
S A M E |
Totals |
n = # Cells | I_{t} = I_{o} × n | Iτ_{t} = Iτ_{o} × n | V_{t} = V_{o} | ε_{t} = ε_{o} × n |
Individual Cells |
n = # Cells | I_{i} = I_{o} | Iτ_{i} = Iτ_{o} | V_{i} = V_{o} | ε_{i} = ε_{o} | ||
P A R − S E R |
S A M E |
Totals |
n ^{2} = # Cells
n = # Cells / Series n = # of Series |
I_{t} = I_{o} × n | Iτ_{t} = Iτ_{o} × n | V_{t} = V_{o} × n | ε_{t} = ε_{o} × n ^{2} |
Individual Cells |
R_{i} = R_{o} | I_{i} = I_{o} | V_{i} = V_{o} | ε_{i} = ε_{o} | |||
LINKS: