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Calculate the effective resistance of the resistors shown in this circuit diagram - Leaving Cert Physics - Question e - 2015

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Calculate the effective resistance of the resistors shown in this circuit diagram. ![Circuit Diagram](URL-to-image)

Worked Solution & Example Answer:Calculate the effective resistance of the resistors shown in this circuit diagram - Leaving Cert Physics - Question e - 2015

Step 1

Identify the Circuit Configuration

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Answer

In the given circuit, we have two resistors, 20 Ω and 5 Ω, connected in parallel. To find the effective resistance (

ReffR_{eff}

) of resistors in parallel, we can use the formula:

1Reff=1R1+1R2\frac{1}{R_{eff}} = \frac{1}{R_1} + \frac{1}{R_2}

where:

  • R1=20ΩR_1 = 20 Ω
  • R2=5ΩR_2 = 5 Ω

Step 2

Apply the Formula

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Answer

Substituting the values of the resistors into the formula:

1Reff=120+15\frac{1}{R_{eff}} = \frac{1}{20} + \frac{1}{5}

Calculating the right side, we first convert the fractions to a common denominator:

120+15=120+420=520\frac{1}{20} + \frac{1}{5} = \frac{1}{20} + \frac{4}{20} = \frac{5}{20}

Step 3

Calculate the Effective Resistance

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Answer

Thus, we have:

1Reff=520\frac{1}{R_{eff}} = \frac{5}{20}

To find ReffR_{eff}, we take the reciprocal:

Reff=205=4ΩR_{eff} = \frac{20}{5} = 4 Ω

Therefore, the effective resistance of the resistors in the circuit is 4 Ω.

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