How to Calculate Total Current

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The easiest way to picture a series circuit connection is a chain of elements. The elements are added consequently and in the same line. There is only one path wherein the electrons and charges can flow. Once you have a basic idea of what a series circuit connection involves, you can learn how to calculate total current.

Part 1
Part 1 of 4:

Understanding the Basic Terminology

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  1. Current is the flow of electrically charged carriers like electrons or the flow of charge per unit of time. But what is a charge and what is an electron? An electron is a negatively charged particle. A charge is a property of matter that is used to classify whether a thing is positive or negatively charged. Like magnets, alike charges repel and opposites attract. [1]
    • We can illustrate this by using water. Water is composed of the molecule, H2O – which stands for 2 atoms of Hydrogen and 1 atom of Oxygen bonded together. We know that the oxygen atom and hydrogen atoms make up the molecule, H2O.
    • A flowing body of water is composed of millions and millions of this molecule. We can compare the flowing body of water to the current; the molecule to electron; and the charge to the atoms.
  2. Voltage is the “force” that drives the current to flow. To best illustrate voltage; we will use the battery as an example. Inside the battery is a series of chemical based reactions which create a buildup of electrons in the positive terminal of the battery. [2]
    • If we now connect a medium (eg a wire) from the positive terminal to the negative terminal of the battery, the electron buildup will now move to get away from each other because as we said, alike charges repel.
    • In addition, because of the law of conservation of charge, which states that the net charge of an isolated system should remain constant, the electrons will try to balance the charges by going from the higher concentration of electrons to the lower concentration of electrons or positive terminal to the negative terminal, respectively.
    • This movement causes a potential difference in each of the terminals which we can now call voltage.
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  3. Resistance, on the other hand, is the opposition of certain elements to flow of charge. [3]
    • Resistors are elements with significant resistance. They are placed in certain parts of a circuit to regulate the flow of charge or electrons.
    • If there are no resistors, the electrons are not regulated, the equipment may receive too much charge and it will be damaged or cause a fire due to overcharging.
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Part 2
Part 2 of 4:

Finding Total Current of a Series Circuit Connection

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  1. Imagine a straw you are drinking from. Pinch it several times. What do you notice? The water flowing will be lessened. Those pinches are the resistors. They block the water which is the current. Since the pinches are in a straight line, they are in series. Drawing from this example, the total resistance of resistors in a series is: [4]
    • R(total) = R1 + R2 + R3.
  2. Most of the time, the total voltage is readily given, but in cases where individual voltages are given, we can use the equation: [5]
    • V(total) = V1 + V2 + V3.
    • But why is this so? Using the straw analogy again, after pinching the straw, what do you expect? You need more effort to get water through the straw. The total effort you are delivering is brought about by the individual force the individual pinches need.
    • The “force” you need is the voltage, because it drives the flow of water or the current. Therefore it is only logical that the total voltage is brought about by adding up the individual voltages across each resistor.
  3. Using the straw analysis again, even in the presence of pinches, did the amount of water you get change? No. Although the speed at which you are getting the water changes, the amount of water you can drink is fixed. And if you look closer at the amount of water entering and leaving, the pinches are the same because of the fixed speed the water is flowing, therefore, we can say that: [6]
    • I1 = I2 = I3 = I(total)
  4. But it doesn't stop there! Remember we don't have any of this data, so we can use the Ohm's Law which relates voltage, current and resistance: [7]
    • V = IR.
  5. Three resistors, R1 = 10Ω R2=2Ω R3 = 9Ω, are connected in series. A total voltage of 2.5V is applied to the circuit. Compute for the total current of the circuit. First let's compute for the total resistance: [8]
    • R(total) = 10Ω R2 + 2Ω R3 + 9Ω
    • Therefore R(total) = 21Ω
  6. [9]
    • V(total) = I(total) x R(total) .
    • I(total) = V(total) / R(total) .
    • I(total) = 2.5V / 21Ω .
    • I(total) = 0.1190A .
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Part 3
Part 3 of 4:

Finding Total Current of Parallel Circuits

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  1. Like it name, a parallel circuit contains elements that are arranged in a parallel way. This makes use of multiple wiring arrangements creating paths wherein current can travel. [10]
  2. Since we have sorted out the terminologies in a previous section, we can now go directly to the computations. Take for an example a pipe split into two paths with different diameters. For the water to flow into both of the pipes, do you need to use unequal forces in each of the pipes? No. You just need enough force for the water to flow. Therefore, using the analogy that the water is the current and the force is the voltage, we can say that: [11]
    • V(total) = V1 + V2 + V3 . [12]
  3. Say you want to regulate the water flowing in the pipes. How will you block the pipes? Do you put just one blockage on each path or do you put multiple blockages arranged consecutively to control the water flow? You would need to do the latter. For resistances, this analogy is the same. Resistors connected in series regulate current far better than those arranged in a parallel way. The equation for the total resistance in a parallel circuit is: [13]
    • 1/R(total) = (1/R1) + (1/R2) + (1/R3) .
  4. Going back to our example, the water flowing from the source to the split path is divided. The same is applicable for current. Since there are multiple paths where charges can flow, it can be said that to be split. The pathways do not necessarily receive equal amounts of charge. It is dependent on the resistances and the materials the elements have in each path. Therefore, the equation of the total current is just the summation of all the currents in all of the paths: [14]
    • I(total) = I1 + I2 + I3.
    • Of course, we can't use this yet because we do not have the individual currents. In this case Ohm's Law can also be used.
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Part 4
Part 4 of 4:

Solving an Example of Parallel Circuits

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  1. 4 resistors divided into two paths which are connected in parallel. Path 1 contains, R1 = 1Ω R2=2Ω while Path 2 contains, R3 = 0.5Ω R4=1.5Ω. The resistors in each path are connected in series. The voltage applied in path 1 is 3V. Find the total current.
  2. Since the resistors in each path are connected in series, we will find solve for the total resistance in each path.
    • R(total 1&2) = R1 +R2 .
    • R(total 1&2) = 1Ω + 2Ω .
    • R(total 1&2) = 3Ω .
    • R(total 3&4) = R3 + R4 .
    • R(total 3&4) = 0.5Ω + 1.5Ω .
    • R(total 3&4) = 2Ω.
  3. Now, we since the paths are connected in parallel, we will now use the equation for parallel connection
    • (1/R(total)) = (1/R(total 1&2)) + (1/R(total 3&4)) .
    • (1/R(total)) = (1/3Ω) + (1/2Ω) .
    • (1/R(total)) = ⅚ .
    • R(total) = 1.2Ω.
  4. Now compute for the total voltage. Since the total voltage is equal to all the voltages:
    • V(total) = V1 = 3V .
  5. Now, we can compute for the total current using Ohm's Law.
    • V(total) = I(total) x R(total) .
    • I(total) = V(total)/R(total) .
    • I(total) = 3V/1.2Ω .
    • I(total) = 2.5A .
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  • Question
    How do you calculate resistors connected in a series?
    Community Answer
    Series resistors' value is the value of all added together. 1 Ohm+2 Ohm = 3 Ohm total, for example.
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  • Question
    What is the formula for a total current?
    Gabeericwolf
    Community Answer
    IT = VT/RT or I total = V total / R total or the total current = the total voltage / the total resistance.
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  • Question
    A street lamp is rated at 240V and 120W. How do I calculate the current through the lamp when it is working at its recommended power?
    Community Answer
    The answer is 0.5 amps. Using the P=IxE formula, I=P/E so plugging the numbers in gives 120W/240V=0.5 Amps
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      • The total resistance for the parallel circuit is always smaller than ANY of the resistance of the resistors.
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      • Terminologies:
        • Circuit – composed of elements (e.g. resistors, capacitors, and inductors) connected by wires and wherein current can pass through.
        • Resistors – elements that can reduce or resist current
        • Current – flow of charge into wires; unit: Ampere, A
        • Voltage – work done per unit charge; unit: Voltage, V
        • Resistance – measurement of the opposition of an element to electric current; unit: Ohm, Ω
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      References

      1. ↑ https://www.physicsclassroom.com/class/circuits/Lesson-2/Electric-Current
      2. ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-1/voltage-current/
      3. ↑ https://www.physicsclassroom.com/class/circuits/Lesson-3/Resistance
      4. ↑ https://www.grc.nasa.gov/www/k-12/airplane/ohmrpar.html
      5. ↑ https://www.grc.nasa.gov/www/k-12/airplane/ohmrpar.html
      6. ↑ https://www.khanacademy.org/science/physics/circuits-topic/circuits-resistance/v/circuits-part-3
      7. ↑ https://www.khanacademy.org/science/physics/circuits-topic/circuits-resistance/v/circuits-part-2
      8. ↑ https://www.khanacademy.org/science/physics/circuits-topic/circuits-resistance/v/circuits-part-2
      9. ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-current-resistance-relate/
      1. ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-5/simple-parallel-circuits/
      2. ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-5/simple-parallel-circuits/
      3. ↑ https://courses.lumenlearning.com/suny-physics/chapter/19-6-capacitors-in-series-and-parallel/
      4. ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-5/simple-parallel-circuits/
      5. ↑ https://pressbooks.bccampus.ca/basicelectricity/chapter/ground/

      About This Article

      Article Summary X

      To find the total current in both series and parallel circuits, start by calculating the total resistance. For series circuits, the total resistance is equal to resistor 1 plus resistor 2 plus resistor 3 and so forth. For parallel circuits, the inverse of the total resistance is equal to the inverse of resistor 1 plus the inverse of resistor 2 and so forth. Calculate the total voltage of the circuit next. In both series and parallel circuits, the total voltage is equal to the sum of the individual voltages. Once you have worked out the total resistance and voltage, use Ohm’s Law to calculate the total current in the circuit. In Ohm’s Law, the total current is equal to the total voltage divided by the total resistance. In a series circuit, the current is the same through all of the components in the circuit, whereas in a parallel circuit, the total current is only equal to the individual current in that branch of the circuit. For more information on calculating the total current, like how to understand the difference between voltage and current, read on!

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