A potentiometer is essentially a resistor with three contacts, one of which is m

Question

A potentiometer is essentially a resistor with three contacts, one of which is mobile. It acts as a variable resistor, since changing the position of the mobile contact called the "wiper" (denoted by an arrow) changes the amount of the resistor through which current must pass. The circuit to the right consists of one 82.6 V battery, one fixed resistor, and one potentiometer. In addition, one of the wires is grounded (at zero potential). 1480 The resistive material inside the potentiometer has a resistance of 475 Ohms per millimeter. To what distance x should the wiper be moved so that 16.8 milliamps of current pass through point B? Number With the wiper in this position, what is the potential at point B Number

Explanation / Answer

i) What is the total circuit resistance that results in a current of 16.8 mA when a voltage of 82.6 volts is applied across it?

Ohm's Law gives us:
r = v/i = (82.6 volts / 0.0168 amps) = 4917 ohms

This is made up of a fixed resistor of 1480 ohms in series with the unknown resistance of the potentiometer (Rp).

Resistances in series just add. So 1480 + Rp = 4917
Potentiometer resistance = (4917 - 1480) = 3437 ohms

(3437 ohms / 475 ohms/mm) = 7.23 mm

ii) What is the potential difference across a 1480 ohm resistor when 16.8 mA flows through it?

Ohm's Law again:
v = i * r = (0.0168 amp * 1480 ohms) = 24.9 volts

The top end of the fixed resistor is grounded, so it is at a potential of 0 V.
It is also shown as connected to the positive terminal of the battery.

So if the p.d. across the fixed resistor is 24.9 V, point B must be at a potential of -24.9 volts.

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