The basic idea behind transformers is that they take a certain input voltage and

Question

The basic idea behind transformers is that they take a certain input voltage and either amplify it or reduce it. This is done via magnetic induction. Consider this simple model: Two solenoids of equal length share a central axis, with the smaller radius solenoid sitting inside the larger radius one (we call the solenoids are "coaxial"). The smaller solenoid has 1100 turns while the larger one has 4000 turns. The smaller solenoid is connected to a time-varying power source of peak voltage 5. (P1) What is the peak back emf in the first solenoid (note that it can be thought of as an inductor)? (P2) What is the peak induced emf in the larger solenoid due to the varying magnetic field in the smaller solenoid (HINT: your answer should reveal a relatively simple relationship between the ration of the number of turns of the two solenoids and the relationship between the peak voltages of the two solenoids)?

Explanation / Answer

The relations between current, voltage and number of turns is given by:

Is/Ip = Vp/Vs = Np/Ns

In this problem:

Np = 4000

Ns = 1100

Vs = 5

Solve for Vp = 18.18

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