DP 3-1 The circuit shown in Figure DP 3.1 uses a potentiometer to produce a variable voltage. The voltage v_m varies as a knob connected to the wiper of the potentiometer is turned. Specify the resistances R₁ and R₂ so that the following three requirements are satisfied:

1. The voltage v_m varies from 8 V to 12 V as the wiper moves from one end of the potentiometer to the other end of the potentiometer.

2. The voltage source supplies less than 0.5 W of power.

3. Each of R₁, R₂, and R_P dissipates less than 0.25 W.

Figure DP 3.1

So redraw the circuit to show the voltage division we have

So the voltage read by the meter is found from current division

a is the amount of the wiper of the potentiometer is turned. a = 0 it is not turned from the minimum and a = 1 it is turned all the way. When a = 0, the voltmeter is only seeing the resistance R2. So the voltage division is

And

When a = 1, we get

Power supplied by the voltage source is

Rearranging the two voltage divider questions we can create the following three equations must hold

There are many possible values that will satisfy all three of these equations. To get one set, choose an Rp

Then

Solving for

Check Power

Power supplied is sum of these

Many Possible Answers One Choice

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This page last updated on January 22, 2019