A solenoid of length 10 cm and 100 turns is wound over a magnetic...

To demagnetize the core, the magnetic intensity $H$ produced by the solenoid must be equal to the coercivity of the core material.

Given:
Coercivity $H_c = 2000$ A m$^{-1}$
Length of solenoid $L = 10$ cm $= 0.1$ m
Number of turns $N = 100$

The magnetic intensity is given by $H = ni = \dfrac{N}{L}i$.

Substituting the given values:
$2000 = \dfrac{100}{0.1} \times i$
$2000 = 1000 \times i$
$i = 2$ A.

The total resistance of the series circuit is $R_{total} = R + R_{solenoid} + r$, where $R_{solenoid} = 2$ $\Omega$ and $r = 1$ $\Omega$.

Using Ohm's law for the complete circuit:
$V = i \times R_{total}$
$20 = 2 \times (R + 2 + 1)$
$10 = R + 3$
$R = 7$ $\Omega$.

Answer: $7$