Physics

Problem

A circuit consists of two fixed resistors of

3\,\Omega

and

9\,\Omega

connected in series with a variable resistor

R_{\text v}

that can be adjusted from

0\,\Omega

12\,\Omega

. The combination is connected across a

24\,\text{V}

battery of negligible internal resistance. a. (i) Write an expression for the total resistance

R_{\text{eq}}

of the circuit in terms of

R_{\text v}

. b. (ii) Determine the minimum and maximum values of

R_{\text{eq}}

R_{\text v}

is varied through its range. c. (iii) For each extreme value of

R_{\text{eq}}

, calculate the corresponding current drawn from the battery.

Intuitive explanation

The key is recognizing that total resistance changes as you adjust $R_{\text{v}}$ , which directly changes the current flowing through the entire series circuit, and therefore the voltage drops across each component. Since the fixed resistors are always in series with the variable one, their combined resistance forms the denominator in Ohm's law—so you're really tracking how the circuit's total resistance varies and how that ripples through to affect power dissipation or voltage distribution. The variable resistor acts as a "control knob" for the whole circuit's behavior.

Intuitive explanation

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