Question

Calculate the ratio of equivalent resistance between series and parallel combination of 10 ohm, 20 ohm and 30 ohm.​

Answer 1

Given :

• First Resistance (R1) = 10 ohm
• Second Resistance (R2) = 20 ohm
• Third Resistance (R3) = 30 ohm

To Find :

• Equivalent resistance in series as well as in parallel.

Solution :

As we know that formula for calculating equivalent resistance in series is :

⇒Rs = R1 + R2 + ......... + Rn

⇒Rs = R1 + R2 + R3

⇒Rs = 10 + 20 + 30

⇒Rs = 10 + 50

⇒Rs = 60

$\therefore$ Equivalent Resistance in series is 60 ohm.

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Now, use formula for equivalent resistance in parallel :

⇒1/Rp = 1/R1 + 1/R2 + ......... + 1/Rn

⇒1/Rp = 1/R1 + 1/R2 + 1/R3

⇒1/Rp = 1/10 + 1/20 + 1/30

⇒1/Rp = (6 + 3 + 2)/60

⇒1/Rp = 11/60

⇒Rp = 60/11

⇒Rp = 5.45 (approx.)

$\therefore$ Equivalent resistance in parallel is 5.45 ohm (approx.)

Answer 2

$\purple{\sf{Answer:-}}$

R1 = 10 Ω

R1 = 10 ΩR2 = 20 Ω

R1 = 10 ΩR2 = 20 ΩR3 = 30 Ω

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• Equivalent resistance in series as well as in parallel.

Rs = R1 + R2 + ......... + Rn

Rs = R1 + R2 + R3

Rs = 10 + 20 + 30

Rs = 10 + 50

Rs = 60Ω

Equivalent Resistance in series is 60 Ω

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• Equivalent resistance in parallel :

1/Rp = 1/R1 + 1/R2 + ......... + 1/Rn

1/Rp = 1/R1 + 1/R2 + 1/R3

1/Rp = 1/10 + 1/20 + 1/30

1/Rp = (6 + 3 + 2)/60

1/Rp = 11/60

Rp = 60/11

Rp = 5.4545 (approx.)

Equivalent resistance in parallel is 5.455Ω (approx.)

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Equivalent Resistance in series is 60 Ω

Equivalent resistance in parallel is 5.455Ω (approx.)

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