ELECTROMAGNETISM & RELATIVITY - Chapter 3, Exercise 1 Solution
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Finding Resistance from Voltage and Current (Ohm's Law)

PROBLEM
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A 9 V battery drives a current of 0.5 A through a resistor. Using
Ohm's law, calculate the resistor's resistance.

SOLUTION
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Starting from Ohm's law:

    V = IR

Rearranged to solve for resistance:

    R = V / I

Substitute the given values:

    V = 9 V
    I = 0.5 A

    R = 9 / 0.5
    R = 18 ohms

ANSWER: The resistor's resistance is 18 ohms.

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WHY THIS WORKS AS AN ANSWER

Ohm's law relates all three circuit quantities (voltage, current, and
resistance) in one simple proportional relationship - given any two,
the third is found directly by rearranging V = IR. Here, a
comparatively low current (0.5 A) resulting from a moderate voltage
(9 V) indicates a genuinely fairly high resistance (18 ohms) is
present in the circuit, exactly matching the physical intuition that
resistance is what "resists" or limits current flow for a given
voltage.