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NVAEasyJEE 2023Combination of Resistors

JEE Physics 2023 Question with Solution

10 resistors each of resistance 10 Ω10 \, \Omega can be connected to get maximum and minimum equivalent resistance. The ratio of maximum to minimum equivalent resistance is:

Answer

Correct answer:100

Step-by-step solution

Series and Parallel Combination

Given: There are 1010 resistors, each of resistance 10 Ω10 \, \Omega.

Find: The ratio of maximum equivalent resistance to minimum equivalent resistance.

Maximum equivalent resistance is obtained when all resistors are connected in series:

Rmax=10R=10×10=100 ΩR_{\text{max}} = 10R = 10 \times 10 = 100 \, \Omega

Minimum equivalent resistance is obtained when all resistors are connected in parallel:

Rmin=R10=1010=1 ΩR_{\text{min}} = \frac{R}{10} = \frac{10}{10} = 1 \, \Omega

Now the required ratio is:

RmaxRmin=1001=100\frac{R_{\text{max}}}{R_{\text{min}}} = \frac{100}{1} = 100

Therefore, the required ratio is 100100.

Common mistakes

  • Assuming maximum resistance occurs in parallel. This is wrong because parallel combination reduces equivalent resistance. For maximum value, all resistors must be connected in series.

  • Using 10R10R for the minimum resistance. This is incorrect because identical resistors in parallel give Rn\frac{R}{n}, not nRnR. Here the minimum resistance is 1010\frac{10}{10}.

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