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Calculating total circuit resistance is a fundamental aspect of electrical engineering and is crucial in designing and analyzing circuits. Total circuit resistance refers to the overall impedance or opposition to the flow of electric current in a circuit. It determines the amount of current that can flow through the circuit and affects the performance and efficiency of electrical systems. To accurately calculate total circuit resistance, an understanding of Ohm’s law, series and parallel resistors, and circuit simplification techniques is essential. In this guide, we will delve into the various methods and formulas used to calculate total circuit resistance, providing step-by-step explanations and practical examples to help you confidently navigate through complex circuit 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] XResearch 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] XResearch 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] XResearch 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] XResearch 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] XResearch sourcehyperphysics.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 an essential skill in electrical engineering and circuit analysis. By understanding the concepts of resistance and how it affects the flow of current in a circuit, engineers can determine the overall resistance of a circuit and make informed decisions about the design and performance of electrical systems. Through various methods such as series and parallel resistances, Ohm’s Law, and Kirchhoff’s laws, engineers can accurately calculate the total resistance. This knowledge enables them to optimize circuit functionality, prevent overload or overheating, and ensure the safe and efficient operation of electrical systems. Overall, the ability to calculate total circuit resistance is a fundamental aspect of electrical engineering that plays a crucial role in designing and analyzing circuits.
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