For example, a series circuit has a 2 Ω (ohm) resistor, a 5 Ω resistor, and a 7 Ω resistor. The total resistance of the circuit is 2 + 5 + 7 = 14 Ω.
The current of a series circuit is the same at all points on the circuit. [2] X Research source If you know the current at any point, you can use that value in this equation. The total voltage is equal to the voltage of the supply (the battery). It is not equal to the voltage across one component. [3] X Research source
For example, a series circuit is powered by a 12 volt battery, and the current is measured at 8 amps. The total resistance across the circuit must be RT = 12 volts / 8 amps = 1. 5 ohms.
If your circuit has resistors on the main path (before or after the branched area), or if there are two or more resistors on a single branch, Skip down to the combination circuit instructions instead.
For example, a parallel circuit has three branches, with resistances of 10 Ω, 2 Ω, and 1 Ω. Use the formula 1RT=110+12+11{\displaystyle {\frac {1}{R_{T}}}={\frac {1}{10}}+{\frac {1}{2}}+{\frac {1}{1}}} and solve for RT:Convert fractions to a common denominator: 1RT=110+510+1010{\displaystyle {\frac {1}{R_{T}}}={\frac {1}{10}}+{\frac {5}{10}}+{\frac {10}{10}}}1RT=1+5+1010=1610=1. 6{\displaystyle {\frac {1}{R_{T}}}={\frac {1+5+10}{10}}={\frac {16}{10}}=1. 6}Multiply both sides by RT: 1 = 1. 6RTRT = 1 / 1. 6 = 0. 625 Ω.
In a parallel circuit, the voltage across one branch is the same as the total voltage across the circuit. [4] X Research source As long as you know the voltage across one branch, you’re good to go. The total voltage is also equal to the voltage of the circuit’s power source, such as a battery. In a parallel circuit, the current may be different along each branch. You need to know the total current, or you won’t be able to solve for total resistance.
For example, a parallel circuit has a voltage of 9 volts and total current of 3 amps. The total resistance RT = 9 volts / 3 amps = 3 Ω.
In practical applications, this usually means a resistor has failed or been bypassed (short-circuited), and the high current could damage other parts of the circuit. [5] X Research source
For example, a circuit has a 1 Ω resistor and a 1. 5 Ω resistor connected in series. After the second resistor, the circuit splits into two parallel branches, one with a 5 Ω resistor and the other with a 3 Ω resistor. Circle the two parallel branches to separate them from the rest of the circuit.
The example circuit has two branches with resistance R1 = 5 Ω and R2 = 3 Ω. 1Rparallel=15+13{\displaystyle {\frac {1}{R_{parallel}}}={\frac {1}{5}}+{\frac {1}{3}}}1Rparallel=315+515=3+515=815{\displaystyle {\frac {1}{R_{parallel}}}={\frac {3}{15}}+{\frac {5}{15}}={\frac {3+5}{15}}={\frac {8}{15}}}Rparallel=158=1. 875{\displaystyle R_{parallel}={\frac {15}{8}}=1. 875}Ω
In the example above, you can ignore the two branches and treat them as one resistor with resistance 1. 875Ω.
The simplified diagram has a 1 Ω resistor, 1. 5 Ω resistor, and the section with 1. 875 Ω you just calculated. These are all connected in series, so RT=1+1. 5+1. 875=4. 375{\displaystyle R_{T}=1+1. 5+1. 875=4. 375}Ω.
Remember, when solving for total resistance, you need to know the total power of the circuit. It’s not enough to know the power flowing through one component.
P = VI (power = voltage x current) Ohm’s Law tells us that V = IR. Substitute IR for V in the first formula: P = (IR)I = I2R. Rearrange to solve for resistance: R = P / I2. In a series circuit, the current across one component is the same as the total current. This is not true for a parallel circuit.
P = VI Rearrange Ohm’s Law in terms of I: I = V / R. Substitute V / R for I in the power formula: P = V(V/R) = V2/R. Rearrange to solve for resistance: R = V2/P. In a parallel circuit, the voltage across one branch is the same as the total voltage. This is not true for a series circuit: the voltage across one component is not the same as the total voltage. Alternatively, you can isolate the circuit and physically test resistance using a multimeter. [10] X Expert Source Marvin WooLicensed Electrician Expert Interview. 31 January 2022.
