How to Solve a Series Circuit: 3 Steps

Table of contents:

How to Solve a Series Circuit: 3 Steps
How to Solve a Series Circuit: 3 Steps
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A series circuit is simple to make. You have a voltage generator, and a current flowing from the positive to the negative terminal, passing through the resistors. In this article we will examine the current intensity, voltage, resistance and power of a single resistor.

Steps

Solve a Series Circuit Step 1
Solve a Series Circuit Step 1

Step 1. The first step is to identify the voltage generator, which is expressed in Volts (V), although it can sometimes be indicated with the symbol (E)

Step 2. At this point we need to examine the values provided for the other elements of the circuit

  • There total resistance of the circuit is obtained simply by adding the contributions of the single resistors.

    R = R1 + R2 + R3 etc …

    Solve a Series Circuit Step 2Bullet1
    Solve a Series Circuit Step 2Bullet1

  • To determine the total current intensity flowing along the circuit, Ohm's law I = V / R can be used. (V = generator voltage, I = total current intensity, R = total resistance) Being a series circuit, the current flowing through each resistor will coincide with the total current flowing through the circuit.

    Solve a Series Circuit Step 2Bullet2
    Solve a Series Circuit Step 2Bullet2

  • There voltage across each resistor it can be calculated using Ohm's law V '= IR' (V '= voltage across the resistor, I = intensity of current flowing through the resistor or circuit (they coincide), R' = resistance of the resistor).

    Solve a Series Circuit Step 2Bullet3
    Solve a Series Circuit Step 2Bullet3

  • There power absorbed by a resistor can be calculated using the formula

    P '= I2R '(P' = power absorbed by the resistor, I = intensity of current flowing through the resistor or circuit (coincide), R '= resistance of the resistor).

    Solve a Series Circuit Step 2Bullet4
    Solve a Series Circuit Step 2Bullet4

  • L' Energy absorbed by the resistors is equal to P * t (P = power absorbed by the resistor, t = time expressed in seconds).

    Solve a Series Circuit Step 2Bullet5
    Solve a Series Circuit Step 2Bullet5

Step 3. Example:

Let's consider a series circuit consisting of a 5 Volt battery, and three resistors of 2 ohm respectively (R.1), 6 ohm (R2) and 4 ohms (R.3). You will have:

  • Total Resistance (R) = 2 + 6 + 4 = 12 Ohm

    Solve a Series Circuit Step 3Bullet1
    Solve a Series Circuit Step 3Bullet1

  • Total Current Intensity (I) = V / R = 5/12 = 0.42 Ampere.

    Solve a Series Circuit Step 3Bullet2
    Solve a Series Circuit Step 3Bullet2

  • Voltage across the resistors

    Solve a Series Circuit Step 3Bullet3
    Solve a Series Circuit Step 3Bullet3
    1. Voltage across R1 = V1 = I x R1 = 0.42 x 2 = 0.84 Volt
    2. Voltage across R2 = V2 = I x R2 = 0.42 x 6 = 2.52 Volts
    3. Voltage across R3 = V3 = I x R3 = 0.42 x 4 = 1.68 Volt

    4. Power absorbed by the resistors

      Solve a Series Circuit Step 3Bullet4
      Solve a Series Circuit Step 3Bullet4
      1. Power absorbed by R.1 = P1 = I2 x R1 = 0.422 x 2 = 0.353 Watt
      2. Power absorbed by R.2 = P2 = I2 x R2 = 0.422 x 6 = 1.058 Watt
      3. Power absorbed by R.3 = P3 = I2 x R3 = 0.422 x 4 = 0.706 Watt

      4. Energy absorbed by the resistors

        Solve a Series Circuit Step 3Bullet5
        Solve a Series Circuit Step 3Bullet5

        1. Energy absorbed by R.1 in, say, 10 seconds

          = E1 = P1 x t = 0.353 x 10 = 3.53 Joules

        2. Energy absorbed by R.2 in, say, 10 seconds

          = E2 = P2 x t = 1.058 x 10 = 10.58 Joules

        3. Energy absorbed by R.3 in, say, 10 seconds

          = E3 = P3 x t = 0.706 x 10 = 7.06 Joules

Suggestions

  • If the internal resistance of the voltage source (r) is also indicated, this must be added to the total resistance of the circuit (V = I * (R + r))
  • The total voltage of the circuit is obtained by adding the voltages across the individual resistors connected in series.

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