A wire of resistance 20Ω20Ω is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _____ ΩΩ.
Question
A wire of resistance 20Ω20Ω is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _____ ΩΩ.
Solution
Step 1: The wire of resistance 20Ω is divided into 10 equal parts. So, the resistance of each part is 20Ω/10 = 2Ω.
Step 2: Two parts are connected in parallel. The equivalent resistance (R_parallel) of two resistors of equal resistance (R) connected in parallel is given by R_parallel = R/2. So, the equivalent resistance of two parts connected in parallel is 2Ω/2 = 1Ω.
Step 3: The resulting pairs of parallel combination are connected in series. Since there were 10 parts originally, there will be 5 pairs of parallel combinations. The equivalent resistance (R_series) of resistors connected in series is the sum of the resistances. So, the equivalent resistance of the final combination is 5 * 1Ω = 5Ω.
So, the equivalent resistance of the final combination is 5Ω.
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