Question

A solenoid is at potential difference of 60V and current flows through it is 15 amperes, then the resistance of coil will be:
A. $4\mathrm{\Omega }$
B. $8\mathrm{\Omega }$
C. $0.25\mathrm{\Omega }$
D. $2\mathrm{\Omega }$

Answer 1

Hint:Here the potential difference and the current flowing through a solenoid is given and we know the relation between the two by Ohm's law that is both are directly proportional to each other. Then put the value of both the quantity from the question and finally get the required answer for the resistance.

Formula used:
Ohm’ s law: Potential difference is directly proportional to the current flowing is given by:
$V\propto I$
$V=IR$
Where, V is potential difference at the ends of solenoid, I is current flowing in the solenoid and R is the resistance of the solenoid.

Complete step by step solution:
Given information from the question:
Potential difference at the ends of the solenoid coil = $V=60V$
Current flowing through the solenoid coil= $I=15A$
Let the resistance of the solenoid coil given be R.
By Ohm’s law, we get;
$V=IR$
So,
$R={\displaystyle \frac{V}{I}}$
Both the value of potential difference V and current I are given.
Putting the given value, we get;
$R={\displaystyle \frac{60}{15}}=4\mathrm{\Omega }$

Hence, the correct answer is option A.

Note: A long straight wire coil can be used to create a magnetic field that is virtually homogeneous, comparable to that of a bar magnet. Such coils, known as solenoids, have various practical uses. The inclusion of an iron core can substantially enhance the field. These cores are common in electromagnets.