To find the rms value of current in the circuit, we need to calculate the impedance of the inductor and then use Ohm's law.

1. Impedance of the Inductor:
The impedance of an inductor (ZL) is given by the formula ZL = jωL, where j is the imaginary unit, ω is the angular frequency, and L is the inductance.

Given:
Inductance (L) = 35 mH = 35 × 10^(-3) H
Angular frequency (ω) = 2πf, where f is the frequency

Substituting the values, we get:
ω = 2π × 70 Hz = 140π rad/s

Now, calculating the impedance of the inductor:
ZL = jωL = j(140π)(35 × 10^(-3)) = j4.9π

2. Ohm's Law:
Ohm's law states that the current (I) flowing through a circuit is equal to the voltage (V) across the circuit divided by the impedance (Z) of the circuit. Mathematically, it can be written as I = V/Z.

Given:
Voltage (V) = 200 V

Substituting the values, we get:
I = 200 V / j4.9π

To find the rms value of current, we need to take the magnitude of the complex current. The magnitude of a complex number a + bj is given by √(a^2 + b^2).

3. Calculating the Magnitude of Current:
We need to convert the expression for current from polar form (j4.9π) to rectangular form. Using Euler's formula, we have j = e^(jπ/2).

I = 200 V / j4.9π
= 200 V / (e^(jπ/2)4.9π)
= 200 V / (e^(jπ/2) × e^(j4.9π))
= 200 V / e^(jπ/2 + j4.9π)
= 200 V / e^(j(π/2 + 4.9π))
= 200 V / e^(j(5.4π))

Taking the magnitude of the current, we have:
|I| = |200 V / e^(j(5.4π))|
= |200 V / (cos(5.4π) + j sin(5.4π))|
= |200 V / (-1 + j0)|
= |200 V / (-1)|
= |-200 V|
= 200 V

Therefore, the rms value of the current in the circuit is 200 A.

The given options are:
a) 13 A
b) 15 A
c) 20 A
d) 45 A

None of the given options match the calculated rms value of 200 A. Hence, the given options are incorrect.