(1) A transformer is used to operate a model train. The transformer, which is pl

Question

(1) A transformer is used to operate a model train. The transformer, which is plugged into a standard electrical outlet, produces an output voltage of 13.3 V (rms), applied to the train's tracks. (The voltage supplied to transformer from outlet is 120 V.)

(a) What is the ratio of the number of turns in the primary to the number of turns in the secondary?

=

(b) If the train uses an average power of 24.2 W, what are the rms currents in the secondary and in the primary? Assume an ideal transformer, with no energy loss.

Iprimary

Isecondary

(2) Find the cross-sectional area of a 4.8 cm long solenoid with 460 turns and a self-inductance of 36 µH.

(3) Find the magnetic energy stored by a 4.86 mH inductor when the current through it is 10.8 A.

Explanation / Answer

1) a) ratio of the number of turns in the primary to the number of turns in the secondary = Vp/Vs

                                                                                                                         = 120/13.3 = 9.022

   b)    Iprimary   =   24.2/120 = 0.2016 A

           Isecondary   =   24.2/13.3 = 1.819 A

2)    Here, L = uoN2A/L

=>    36 * 10-6 = (4 * 3.14 * 10-7 * 460 * 460 * A)/0.048

=>   cross-sectional area , A =   6.5018 * 10-6 m2

3)     magnetic energy stored =   1/2LI2

                                                        = 1/2 * 4.86 * 10-3 * 10.8 * 10.8

                                              = 0.2834 J

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