Question

3. A string of fifty 15 ohm Christmas tree lights are connected in series. One burns out, they all burn out. Calculate the total resistance.

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Answer 1

Given

• 50 lamps are connected in series
• Resistance = 15Ω

To Find

• Equivalent resistance

Solution

☯ The equivalent resistance of a series combination is given by, Rₙₑₜ = R₁ + R₂ ... + Rₙ

• Note that here the values of all the resistors are the same

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✭ Equivalent Resistance

→ Rₙₑₜ = R₁ + R₂ ... + Rₙ

• R = 15Ω
• n = 50

→ Rₙₑₜ = 15+15+15+15+15+15+15+15+15+15+15+15 ... + 15 [50 Times]

→ Rₙₑₜ = 15 × 5

→ Rₙₑₜ = 750 Ω

∴ The equivalent Resistance of the combination is 750Ω

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Know More

• Parallel Connection :- 1/Rₙₑₜ = 1/R₁ + 1/R₂ .... 1/Rₙ
• It was given that as one lamp burn all the others were also affected, it is one of the disadvantages of series connection