Question

Calculate the equivalent resistance when three resistances of 2 ohm, 4 ohm and 8ohm are connected parallel​

Answer 1

Given:

• Three resistors are connected in parallel
• Resistor 1 = 2 Ω
• Resistor 2 = 4 Ω
• Resistor 3 = 8 Ω

To find:

• Equivalent resistance

Solution:

As we know that n number of resistors are connected in parallel the equivalent resistance will be

1/Rn or Eq. resistance = 1/R1 + 1/R2 + …… + 1/Rn

Similarly

1/Eq. resistance = 1/R1 + 1/R2 + 1/R3

→ 1/Eq. resistance = 1/2 + 1/4 + 1/8

→ 1/Eq. resistance = 0.5 + 0.25 + 0.125

→ 1/Eq. resistance = 0.2 Ω

→ Eq. resistance = 5Ω

Hence , equivalent resistance = 5Ω

Answer 2

$\rm R_{1}=2 \ ohm \\\\R_{2}=4 \ ohm \\\\R_{3}=8 \ ohm \\\\\rm Equivalent \ resistance \ in \ parralel \ series \ : \ \bf\dfrac{1}{R} =\dfrac{1}{R_{1}} +\dfrac{1}{R_{2}} +\dfrac{1}{R_{3}} \\\\\rm Equivalent \ resistance \ , \ \dfrac{1}{R} =\dfrac{1}{2} +\dfrac{1}{4} +\dfrac{1}{8}$

                                  $\rm \dfrac{1}{R} = \dfrac{4}{8} +\dfrac{2}{8}+ \dfrac{1}{8}$

                                  $\rm \dfrac{1}{R} =\dfrac{7}{8}$

                                  $\rm \bf R=\dfrac{8}{7} \ ohm$

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