How to Solve a Series Circuit: 3 Steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

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

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 …

  

• 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.

  

• 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).

  

• 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).

  

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

  

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

  

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

  

• Voltage across the resistors

  

  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

     

     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

        

        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.