A set of light bulbs is wired in parallel across a 12V battery. You want to calculate the power dissipated by one bulb with resistance 60Ω. Which formula is most natural to apply, and why?
AP = I²R, because current is always the most fundamental quantity in a circuit
BP = V²/R, because all parallel elements share the same voltage
CP = IV, but you must first use Ohm's law to find both I and V independently
DP = I²R, because the same current flows through all parallel elements
In a parallel circuit, all branches share the same voltage (12V here). P = V²/R uses the known voltage directly: P = (12)²/60 = 2.4W. Option D describes a series circuit, not parallel — in a parallel circuit, each branch draws its own current according to its own resistance. P = I²R is more natural in series circuits, where the same current flows through every element.
Question 2 Multiple Choice
A diode allows current to flow easily in one direction but blocks it in the other. Which statement correctly describes a diode in the context of Ohm's law?
AA diode obeys Ohm's law but with a very small resistance in one direction and very large in the other
BA diode is a non-ohmic element — its V-I relationship is not linear, so V = IR does not apply with a fixed constant R
CA diode obeys Ohm's law at all voltages as long as you use the correct R for each direction
DOhm's law is universal and must apply to diodes just as to resistors
A diode is a non-ohmic element: its resistance is not a fixed constant but depends on voltage and current direction. The V-I relationship is exponential, not linear. Ohm's law V = IR only holds for ohmic materials where R is constant. Describing the diode's forward and reverse resistance as 'small' and 'large' (option A) approximates the non-linearity but misrepresents what Ohm's law means — R must be constant for the law to apply.
Question 3 True / False
Ohm's law (V = IR) is a fundamental law of physics that holds for most materials under most conditions.
TTrue
FFalse
Answer: False
Ohm's law is an empirical approximation that holds for ohmic materials over a useful range of conditions. It breaks down for semiconductors (diodes, transistors), for materials at extreme temperatures, and for non-linear elements. It is not derived from first principles but observed — the Drude model provides a physical explanation for why it holds in metals, not a proof that it holds universally. Many important circuit elements are deliberately non-ohmic.
Question 4 True / False
In a series circuit, P = I²R is more natural than P = V²/R because the same current flows through every element.
TTrue
FFalse
Answer: True
In a series circuit, the same current I flows through all elements, while voltage divides across them. When I is the known quantity, P = I²R directly gives power for each element without needing to find individual voltages. Conversely, in a parallel circuit where all elements share the same voltage, P = V²/R is more natural. Both formulas are algebraically equivalent for any ohmic resistor — the choice is about which variable is most directly available.
Question 5 Short Answer
P = I²R and P = V²/R look like different formulas. Why are they actually the same formula, and when would you prefer one over the other?
Think about your answer, then reveal below.
Model answer: Both are derived from P = IV combined with Ohm's law V = IR. Substituting V = IR into P = IV gives P = I²R. Substituting I = V/R gives P = V²/R. They encode the same physics — energy dissipation per unit time in an ohmic resistor — just with different variables expressed. Use P = I²R when current is the known quantity (series circuits). Use P = V²/R when voltage is known (parallel circuits, where all branches share the same V).
The key insight is that these are not independent formulas — they are the same underlying relationship with Ohm's law substituted in different directions. Choosing between them is a matter of which quantity you already know, not which is more correct.