Question

There is a wire of length 20 cm and having resistance 20 ohm is cut into 4 equal pieces and then joined in series. the equivalent resistance is:

(a) 20 ohm
(b) 4 ohm
(c) 5 ohm
(d) 10 ohm

Answer 1

When a wire is cut into four pieces and joined in series, the equivalent resistance is the sum of each piece's resistance. Since each piece has a resistance of 5 ohms, the total equivalent resistance remains 20 ohms.

Step-by-step explanation:

When a wire with a length of 20 cm and a resistance of 20 ohms is cut into 4 equal pieces, each piece will have a length of 5 cm. Considering that resistance is proportional to the length of a wire, each of these pieces will now have a resistance of 5 ohms. When these pieces are joined in series, the total or equivalent resistance of the combination is found by simply adding the resistances of each piece. Therefore, the equivalent resistance when the four pieces are connected in series would be:

5 ohms + 5 ohms + 5 ohms + 5 ohms = 20 ohms

This is still the same as the original resistance of the wire because cutting the wire into pieces and connecting them in series does not change the total resistance. In essence, the wire is still the same total length with the same material properties. Hence, the equivalent resistance remains 20 ohms, not 10 ohms as may have been presupposed.