How to Calculate Total Circuit Resistance

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There are two ways to connect electrical components together. In a series circuit they are connected one after the other while in a parallel circuit they are connected along parallel branches. The way the component resistors are connected determines the overall resistance of the circuit.

Table of Contents

Circuits in series

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Identify series circuits. The series circuit is just a single closed circuit, with no branch circuits. All resistors or other components of the circuit are lined up in a row.

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Add all the resistor values together. In a series circuit, the total resistance of the circuit is equal to the sum of all resistances. ^{[1] X Research Source} The current flowing through all resistors is the same, so each will do its job as it is expected.

Take for example a series circuit with three resistors of 2 Ω (ohms), 5 and 7 Ω respectively. The total resistance of the circuit is 2 + 5 + 7 = 14 Ω.

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We can also start with amperage and voltage. If you don’t know the resistance value of each component, you can rely on Ohm’s Law: V = IR, or voltage = amperage x resistance. The first step is to find the full circuit amperage and voltage:

In a series circuit, the amperage at all points is the same. ^{[2] X Research Source} If you know the amperage at any point, you can use that value for this equation.
The total voltage of the circuit is equal to the voltage of the source (battery). It differs from the voltage of a component in the circuit. ^{[3] X Research Sources}

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Substitute the value in Ohm’s Law. Transform V = IR to find resistance: R = V / I (resistance = voltage / amperage). Substitute the values you find into this formula to find the total resistance.

For example, a series circuit is powered by a 12 volt battery and the measured amperage is 8 amps. The full circuit resistance should be R _T = 12 volts / 8 amps = 1.5 ohms.

Parallel Circuits

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Understand parallel circuits. A parallel circuit divides into many branches, which then recombine. Each branch has a current flowing through it.

If your circuit has resistors located on the main circuit (before or after the branch), or if there are two or more resistors on an individual branch, instead of reading on, skip down to the instructions for the circuit combine.

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Calculate the total resistance of the circuit from the resistance of each branch. Since each resistor only slows down the current flowing through one branch, it has only a small effect on the overall resistance of the circuit. The formula for the total resistance of the circuit _RT is

first

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{displaystyle {frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1}{R_{2}}}+{frac {1}{R_{3 }}}+…{frac {1}{R_{n}}}}

{frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1}{R_{2}}}+{frac {1}{R_{3}} }+...{frac {1}{R_{n}}}

, where, R ₁ is the first branch resistance, R ₂ is the second branch resistance, and so on until the last branch R _n .

For example, consider a parallel circuit with three branches with resistances each of 10 Ω, 2 Ω, and 1 respectively.
Use the formula $first$ $CHEAP$ $BILLION$ $=$ $first$ $ten$ $+$ $first$ $2$ $+$ $first$ $first$ ${displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {1}{2}}+{frac {1}{1}}}$ ${frac {1}{R_{T}}}={frac {1}{10}}+{frac {1}{2}}+{frac {1}{1}}$ and find R _T :
Equivalent denominator: $first$ $CHEAP$ $BILLION$ $=$ $first$ $ten$ $+$ $5$ $ten$ $+$ $ten$ $ten$ ${displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {5}{10}}+{frac {10}{10}}}$ ${frac {1}{R_{T}}}={frac {1}{10}}+{frac {5}{10}}+{frac {10}{10}}$
$first$ $CHEAP$ $BILLION$ $=$ $first$ $+$ $5$ $+$ $ten$ $ten$ $=$ $16$ $ten$ $=$ $first$ $,$ $6$ ${displaystyle {frac {1}{R_{T}}}={frac {1+5+10}{10}}={frac {16}{10}}=1.6}$ ${frac {1}{R_{T}}}={frac {1+5+10}{10}}={frac {16}{10}}=1.6$
Multiply both sides by R _T : 1 = 1.6R _T
R _T = 1 / 1.6 = 0.625 Ω.

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Instead of doing the above, we can start with the amperage and voltage of the whole circuit. If you don’t know the resistance of each part, you’ll need amperage and voltage:

In a parallel circuit, the voltage of each branch is also equal to the voltage of the whole circuit. ^{[4] X Research Source} Just knowing the voltage of a branch, you are ready to go. The full circuit voltage is also equal to the voltage of a power source, such as a battery.
In parallel circuits, the amperage can be different along each branch. You need to know the total amperage, otherwise you won’t be able to find the full circuit resistance.

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Substitute these values in Ohm’s Law. If you know the current and voltage of the circuit, you can find the total resistance using Ohm’s Law: R = V / I.

Take for example a parallel circuit with a voltage of 9 volts and a total current of 3 amps. Full circuit resistance R _T = 9 volts / 3 amp = 3 Ω.

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Be careful with the zero-resistance branch. If a branch in a parallel circuit has no resistance, all current will flow through that branch. The whole circuit resistance is zero ohms.

In practical application this usually indicates a damaged or bypassed resistor (short circuit) and high amperage can damage other parts of the circuit. ^{[5] X Research Sources}

Combination circuit

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Divide your circuit into series and parallel parts. A combination circuit is a circuit in which some components are connected in series (in turn) and others in parallel (on different branches). Look in the circuit diagram for places that can be simplified to a series-only or parallel-only area. Circle each area for easy tracking.

Take for example a circuit with two resistors 1 and 1.5 connected in series. After the second resistor, this circuit splits into two parallel branches, one with a 5 resistor and the other with a 3 resistor.
We circled the two parallel branches to separate them from the rest of the circuit.

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Find the resistance of each parallel section. Using the parallel resistance formula

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{displaystyle {frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1}{R_{2}}}+{frac {1}{R_{3 }}}+…{frac {1}{R_{n}}}}

{frac {1}{R_{T}}}={frac {1}{R_{1}}}+{frac {1}{R_{2}}}+{frac {1}{R_{3}} }+...{frac {1}{R_{n}}}

to find the composite resistance of the single parallel part of the circuit.

The example circuit has two branches with resistors R ₁ = 5 Ω and R ₂ = 3 Ω.
$first$ $CHEAP$ $S$ $S$ $=$ $first$ $5$ $+$ $first$ $3$ ${displaystyle {frac {1}{R_{ss}}}={frac {1}{5}}+{frac {1}{3}}}$ ${frac {1}{R_{{ss}}}}={frac {1}{5}}+{frac {1}{3}}$
$first$ $CHEAP$ $S$ $S$ $=$ $3$ $15$ $+$ $5$ $15$ $=$ $3$ $+$ $5$ $15$ $=$ $8$ $15$ ${displaystyle {frac {1}{R_{ss}}}={frac {3}{15}}+{frac {5}{15}}={frac {3+5}{15}}={frac { 8}{15}}}$ ${frac {1}{R_{{ss}}}}={frac {3}{15}}+{frac {5}{15}}={frac {3+5}{15}}={frac { 8}{15}}$
$CHEAP$ $S$ $S$ $=$ $15$ $8$ $=$ $first$ $,$ $875$ ${displaystyle R_{ss}={frac {15}{8}}=1,875}$ $R_{{ss}}={frac {15}{8}}=1.875$ Ω

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Simplify your circuit diagrams. Once you have found the synergistic resistance of the parallel section, you can cross out the whole section on the diagram. Think of it as a single wire with a resistance equal to the value you just found.

In the example above, you could ignore the two branches and treat them as a 1.875 Ω resistor.

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Add the resistors in series. Once each parallel section has been replaced by a single resistor, the circuit diagram is left with a single loop: a series circuit. The total resistance of a series circuit is equal to the sum of all the individual resistances. Therefore, you just need to accumulate to get the answer.

The schematic has been simplified with 1 Ω, 1.5 resistors and a 1.875 part as you just calculated. They are all connected in series, so $CHEAP$ $BILLION$ $=$ $first$ $+$ $first$ $,$ $5$ $+$ $first$ $,$ $875$ $=$ $4$ $,$ $375$ ${displaystyle R_{T}=1+1.5+1,875=4,375}$ $R_{T}=1+1.5+1,875=4.375$ Ω.

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Use Ohm’s law to find the unknown value. If you don’t know the resistance of a component in a circuit, find a way to calculate it. If the voltage V and the current I passing through the component are known, find the resistance using Ohm’s law: R = V / I.

Use the formula to calculate power consumption

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Learn the formula for calculating power consumption. Power consumption is the level of energy consumption of a circuit and is the level at which the circuit transmits energy to its power supply object (such as a light bulb). ^{[6] X Research source} The total power of the circuit is equal to the product of the total voltage of the circuit with the current of the whole circuit. Or in the form of an equation, we have: P = VI. ^{[7] X Research Sources}

Remember that when finding the total resistance of the circuit, you need to know the total capacity of the circuit. Just the power consumed by one component in the circuit is not enough.

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Use wattage and amperage to find resistance. If you already know these two values, you can combine the two formulas to find the resistance:

P = VI (power = voltage x amperage).
Ohm’s Law says that V = IR.
Substitute IR for V in the first formula: P = (IR)I = I ² R.
Rearrange to find resistance: R = P / I ² .
In a series circuit, the current flowing through any of the components is equal to the total current in the circuit. This is not true for parallel circuits.

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Find resistance from power and voltage. If you only know the wattage and voltage, you can use the same approach to find the resistance. Remember to use the full circuit voltage or the voltage of the source used to power the entire 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) = V ² /R.
Rearrange to find resistance: R = V ² /P.
In a parallel circuit, the voltage of each branch is equal to the total voltage of the circuit. This is not true for series circuits: individual component voltages are not equal to circuit voltages.

Advice

Power is measured in watts (W).
Voltage is measured in volts (V).
Amperage is measured in amps (A), or milliamps (mA). 1 ma = $first$ $*$ $ten$ $-$ $3$ ${displaystyle 1*10^{-3}}$ $1*10^{{-3}}$ A = 0.001 A.
The value of power P used in the above formulas is instantaneous power, that is, power at a specified time. If alternating current (AC) is used, the capacity of the circuit will continuously change. Electricians calculate the average power of an AC circuit using the formula P _average = VIcosθ, where cosθ the power factor of the circuit. ^{[8] X Research source hyperphysics.phy-astr.gsu.edu/hbase/electric/powfac.html#c1}

Steps

Circuits in series

Parallel Circuits

Combination circuit

Use the formula to calculate power consumption

Advice

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