Question

A small diameter, 11 cm long solenoid has 258 turns and is connected in series with a resistor and battery. The size of the magnetic field inside the solenoid is 1.795E-3 T when a voltage of 81.0 V is applied to the circuit. Calculate the resistance of the circuit.

Answer 1

The resistance of the circuit is 133 Ohms

Step-by-step explanation:

Given;

length of the solenoid, L = 11 cm = 0.11 m

number of turns of the solenoid, N = 258 turns

magnetic field inside the solenoid, B = 1.795 x 10⁻³ T

voltage across the solenoid, V = 81.0 V

The magnetic field inside the solenoid is given by;

`B = (\mu_oNI)/(L)`

Where;

I is current through the solenoid

`B = (\mu_oNI)/(L)\\\\I = (BL)/(\mu_o N)\\\\I = ((1.795*10^(-3))(0.11))/((4\pi *10^(-7))(258) )\\\\I = 0.609 \ A`

Apply ohms law to determine the resistance of the circuit.

V = IR

R = V / I

R = (81) / (0.609)

R = 133 Ohms

Therefore, the resistance of the circuit is 133 Ohms