You may use any of the above equations to solve the following. A simple electric

Question

You may use any of the above equations to solve the following.

A simple electrical generator uses a lawn mower engine to produce electricity by rotating a coil of wire in a magnetic field. The coil of wire contains 2000 loops, is circular with a diameter 30cm, and the motor rotates the coil 3600 times per minute in a uniform field with magnitude 1.00mT. The generator produces 17W of power. A transformer is used to convert the voltage output by the generator to 12 V.

a. Calculation: What is the maximum voltage produced by the generator? Please show all your work.

b. Conceptual: Which coil of the transformer has more turns, the primary or secondary (or are they the same)? Please explain.

c. Calculation: What is the maximum current that could be drawn from the transformer by an appliance? Please show all your work.

These are the fundamental equations from the modules we have covered so far. You may use other physics equations from your book, but you must reference where they come from coulomb's law (magnitude of electric force) magnitude of electric field from point charge force on point charge kinematics equations v(t)+at electric potential due to a point charge electric potential difference between points in uniform field (remember that 8 is displacement in the direction of the field) electric potential energy of a point charge capacitor equation effective capacitance (series) effective capacitance (parallel) capacitor potential energy parallel plate capacitor capacitance current current in beam or through wire cylinder resistance temperature dependence of resistivity Ohm's Law effective resistance (series) effective resistance (parallel) resistor dissipated power emf generated power discharging capacitor magnetic force on charge magnetic force on current-carrying wire magnetic torque on current-carrying loop circular motion in magnetic field magnetic field from long straight wire magnetic field at center of circular loop magnetic field inside a solenoid magnetic flux C C1+ C2... Re=R1 + R2 Re R (t) VoeVRC F-NIAB sin electric generator emf transformer equation transformer power induced emf in inductor solenoid inductance inductor potential energy RL circuit (turning on) RL circuit (turning off) Physics Constants emf= NABw sin wt = Io (1-e-n/L) 2 Name Common Symbol 1.602 x 10 1 C 8.99 × 109 N C-2 8.854 x 10-12Fm-1 4 x 10-7 H m-1 3 x 108 ms-1 9.109 x 10-31 kg 1.673 x 10-27kg Elementary Charge Permittivity of Free Space o Permeability of Free Space Speed of Light Electron Mass Proton Mass Unit Conversions electron volt 1 eV = 1.602 × 10-19 J

Explanation / Answer

given

N = 2000 loops

d = 30 cm = 0.3 m

w = 3600 rpm = 3600*2*pi/60 = 377 rad/s

B = 1mT = 1*10^-3 T

a) maximum induced emf = N*A*B*w

= 2000*(pi*0.3^2/4)*1*10^-3*377

= 53.3 volts

b) primary coil should have more turns.
Because we are supposed to use step down transformer.

Vs/Vp = Ns/Np

Vs = (Ns/Np)*Vp

here, Vs(12V) < Vp(53.3v)

so, Ns < Np

c) P_out = V_out*I_out

==> I_out = P_out/V_out

= 17/12

= 1.417 A

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