A wire of 5Ω resistance is drawn out so that its new length is two times the original length. If the resistivity of the wire remains the same and the cross-...
A wire of 5Ω resistance is drawn out so that its new length is two times the original length. If the resistivity of the wire remains the same and the cross-sectional area is halved, the new resistance is
Answer Details
When a wire is stretched, its resistance increases as its cross-sectional area decreases. Similarly, if the wire is compressed, its resistance decreases as the cross-sectional area increases. Also, the resistance of a wire is directly proportional to its length, which means that as the length of a wire increases, its resistance also increases. Here, the wire is drawn out so that its new length is two times the original length. Since the resistivity of the wire remains the same, the resistance of the wire is proportional to its new length. Therefore, the new resistance is 2 times the original resistance. Next, the cross-sectional area of the wire is halved. Since resistance is inversely proportional to the cross-sectional area of a wire, the new resistance is twice the original resistance. Combining the two effects, the new resistance is (2 x 2) times the original resistance, which is 4 times the original resistance. Therefore, the new resistance is 5Ω x 4 = 20Ω. Hence, the answer is 20Ω.