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When it comes to electrical circuits, understanding the concept of resistance is crucial. Resistance is the hindrance that limits the flow of electric current in a circuit. The total resistance in a circuit is the cumulative effect of all the individual resistances within it. By calculating the total circuit resistance, you can determine how much opposition the circuit presents to the flow of current. This knowledge is fundamental for engineers, electricians, and anyone working with circuits, as it allows for the design and analysis of circuits with precision. In this guide, we will explore the step-by-step process of calculating total circuit resistance, including both series and parallel connections, and understand how to apply these calculations in practical situations. Whether you are a beginner looking to grasp the basics or a seasoned professional seeking a refresher, this guide will serve as a comprehensive resource to enhance your understanding of circuit resistance calculations.
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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.
Steps
Circuits in series
- 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.
- 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
- 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
- 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.
- For example, consider a parallel circuit with three branches with resistances each of 10 Ω, 2 Ω, and 1 respectively.
Use the formula firstCHEAPBILLION=firstten+first2+firstfirst{displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {1}{2}}+{frac {1}{1}}} and find R T :
Equivalent denominator: firstCHEAPBILLION=firstten+5ten+tenten{displaystyle {frac {1}{R_{T}}}={frac {1}{10}}+{frac {5}{10}}+{frac {10}{10}}}
firstCHEAPBILLION=first+5+tenten=16ten=first,6{displaystyle {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.
- 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.
- 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.
- 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
- 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.
- The example circuit has two branches with resistors R 1 = 5 Ω and R 2 = 3 Ω.
firstCHEAPSS=first5+first3{displaystyle {frac {1}{R_{ss}}}={frac {1}{5}}+{frac {1}{3}}}
firstCHEAPSS=315+515=3+515=815{displaystyle {frac {1}{R_{ss}}}={frac {3}{15}}+{frac {5}{15}}={frac {3+5}{15}}={frac { 8}{15}}}
CHEAPSS=158=first,875{displaystyle R_{ss}={frac {15}{8}}=1,875} Ω
- In the example above, you could ignore the two branches and treat them as a 1.875 Ω resistor.
- 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 CHEAPBILLION=first+first,5+first,875=4,375{displaystyle R_{T}=1+1.5+1,875=4,375} Ω.
Use the formula to calculate power consumption
- 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.
- 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.
- 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}} 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
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
There are 8 references cited in this article that you can see at the bottom of the page.
This article has been viewed 86,725 times.
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.
In conclusion, calculating the total circuit resistance is a crucial step in understanding and analyzing electrical circuits. By determining the overall resistance, we can evaluate the circuit’s behavior and make informed decisions when designing or troubleshooting electrical systems. Throughout this article, we have explored different ways to calculate total circuit resistance, including the series and parallel resistor combinations. We have also discussed the significance of Ohm’s law and the importance of using proper units and formulas. By applying the formulas and techniques discussed, one can accurately determine the total resistance of a circuit and ensure optimal performance. It is essential to remember that calculating total circuit resistance is not only a mathematical exercise but also a fundamental skill for any electrical engineer or technician.
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