A) \[{{i}_{l}}={{i}_{ll}}={{i}_{lll}}\]
B) \[{{i}_{l}}>{{i}_{ll}}>{{i}_{lll}}\]
C) \[{{i}_{l}}<{{i}_{ll}}<{{i}_{lll}}\]
D) \[({{i}_{l}}={{i}_{lll}})<{{i}_{ll}}\]
Correct Answer: D
Solution :
(d) \[({{i}_{l}}={{i}_{lll}})<{{i}_{ll}}\] We know that, \[R=\rho \frac{l}{A}\] \[\therefore {{R}_{l}}=\rho \frac{L}{A}\] (1) \[{{R}_{ll}}='\rho \frac{1.5L}{A/2}=3\rho \frac{L}{A}\] .(2) \[{{R}_{lll}}=\rho \frac{L/2}{A/2}=\rho \frac{L}{A}\] (3) Using eqs. (1), (2) and (3), we can say that \[{{R}_{ll}}>({{R}_{l}}={{R}_{lll}})\] \[\therefore ({{i}_{l}}={{i}_{lll}})<{{i}_{ll}}\] From Ohm's Law, we know that V = IR when same potential difference is applied \[l\propto \frac{l}{R}\]
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