# Skill Set 21.2

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## Problems

### 1. A loop or wire with a radius of 0.78 m is in the plane of this page, and is rotated so that the loop forms a 23.0 degree angle with the page. If there is a 3.72 T magnetic field into the page, and the rotation takes .015 s, what is the average EMF generated? Which way does it flow? $E = BA\cos \Theta \ / T$

E = ((3.72 T)*((.78 m)2 * 3.14) * (cos 23 - cos 0) / .015 s $E = 37.68 V \approx\ 38 V$

### 2. The wire below is 2.28 m long (really!) and is traveling through a 6.71 T magnetic field out of the page. What is its speed if there exists a potential of 41.6 V from one end to the other? Label the positive end of the wire.

E = B * v * L

41.6 V = (6.71 T) * v * (2.28 m) $v = 2.719 m / s \approx\ 2.72 m/s$

### 3. A transformer has 350 primary windings, and 1600 secondary windings. What is the voltage in the primary if there is a voltage of 512 V (AC) in the secondary?

(Vp / Vs) = (Np / Ns)

(Vp / 512 V) = (350 / 1600)

Vp = 112 V

### 4. You want to step 120 VAC down to 9.6 VAC with a transformer. What should be the number of secondary windings if you have 1800 primary windings?

(Vp / Vs) = (Np / Ns)

(120 V / 9.6 V) = (1800 / Ns)

Ns = 144

### 5. A transformer steps 240 VAC down to 1.5 VAC. What current flows in the secondary if the primary side has 2.6 A flowing through it?

(Vp / Vs) = (Is / Ip)

(240 V / 1.5 V) = (Is / 2.6 A)

Is = 416 A