Solenoid has length L = 1.23m and inner diameter d = 3.55cm. It carries a curren

Question

Solenoid has length L = 1.23m and inner diameter d = 3.55cm. It carries a current i = 5.57 A. It consists of five close-packed layers, each 850 turns along length L. What is the magnetic field at its center? 1.5 uF capacitor is charged to 57V. The charging battery is then disconnected, and a 2MH coil is connected in series with the capacitor so that LC oscillations occur. What is the maximum current in the coil? Assume that the circuit contains no resistance, which would cause the energy to be dissipated. A transformer on a utility pole operates at V_p = 8.5kV on the primary side and supplies electrical energy to a number of nearby houses at V = 120V, both quantities being rms values. Assume an ideal step-down transformer purely resistive load, and a power factor of unity. (a) what is the turns ratio N_p/N_s of the transformer? (b) The average rate of energy consumption (or dissipation) in the houses served by the transformer is 78kW. What are the rms currents in the primary and secondary of the transformer? c)What is the resistive load R_s in the secondary circuit? What is the corresponding? resistive load R_p in the primary circuit? Door bells and buzzers usually are designed for 12-Volt AC and are powered by small transformers which step down 110-Volt AC to 12-Volt AC. Suppose that such a transformer has a primary winding with 1500 turns. How many turns are there on the secondary winding? What is the impedance of this circuit?

Explanation / Answer

1) L , length = 1.23 m

d,diameter = 3.55 cm

I = current = 5.57 A

B ( magnetic field at center) = u0*n*I

n, no of turns per unit length = 5*850 turns / 1.23 m

so B = 4*pi*10-7 *(5*850 turns / 1.23 m) *5.57

B = 0.0241 7T

or B = 24.17 mT

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