High School

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A small exhibition in a shop window is lit by 8 identical bulbs connected to a 60 V power source. The resistance of each bulb is 12.5 Ω.

Calculate the total (equivalent) resistance of the circuit.

Answer :

To solve this problem, we need to calculate the total or equivalent resistance of the circuit when 8 identical bulbs, each with a resistance of 12.5 Ω, are connected to a power source.

In a circuit, the bulbs can be connected in series or parallel configuration. The total resistance calculation will differ based on how they are connected:

  1. Series Connection:

    • In a series circuit, the total resistance [tex]R_{\text{total}}[/tex] is the sum of the individual resistances.
    • Formula: [tex]R_{\text{total}} = R_1 + R_2 + ... + R_8[/tex]
    • Here, as each bulb has a resistance of 12.5 Ω:
      [tex]R_{\text{total}} = 8 \times 12.5 \, \Omega = 100 \, \Omega[/tex]

  2. Parallel Connection:

    • In a parallel circuit, the total resistance [tex]R_{\text{total}}[/tex] can be found using the reciprocal formula:
    • Formula: [tex]\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_8}[/tex]
    • Since all resistances are the same (12.5 Ω), it can be simplified to:
      [tex]\frac{1}{R_{\text{total}}} = 8 \times \frac{1}{12.5}[/tex]
      [tex]\frac{1}{R_{\text{total}}} = \frac{8}{12.5}[/tex]
      [tex]R_{\text{total}} = \frac{12.5}{8} \, \Omega = 1.5625 \, \Omega[/tex]

Based on the type of circuit the bulbs form, use the respective calculation. If the bulbs are connected in parallel, the equivalent resistance of the circuit would be 1.5625 Ω.

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