A long uniform coil of a inductance L henries and associated resistanc...
We know that,
and
when coil is cut into two equal halves,
(Area of cross - section = constant)
So,
Also,
So,
Hence, new values of resistance and inductance which are reconnected in parallel is
and
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A long uniform coil of a inductance L henries and associated resistanc...
**Answer:**
**Explanation:**
When a long uniform coil is cut into two exact halves and rewound in parallel, the resistance and inductance of the combination will be different from the original values.
**Resistance:**
When the coil is cut into two halves and rewound in parallel, the total resistance of the combination decreases. This is because the two halves are now connected in parallel, which reduces the overall resistance.
The resistance of each half is R/2, so when they are connected in parallel, the total resistance becomes:
1/Rt = 1/(R/2) + 1/(R/2) = 2/R
Therefore, the resistance of the combination is R/2.
**Inductance:**
When the coil is cut into two halves and rewound in parallel, the total inductance of the combination also decreases. This is because the two halves are now connected in parallel, which reduces the overall inductance.
The inductance of each half is L, so when they are connected in parallel, the total inductance becomes:
1/Lt = 1/L + 1/L = 2/L
Therefore, the inductance of the combination is L/2.
**Conclusion:**
In conclusion, when a long uniform coil is cut into two exact halves and rewound in parallel, the resistance and inductance of the combination are R/2 and L/2, respectively. Therefore, the correct answer is option 'C'.
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