Test on Which light bulb shines brighter? Power in series and parallel circuits

Question 1: In a series circuit, if two light bulbs are connected, the bulb with the higher resistance will shine brighter.

A. Yes

B. No

Explanation: In a series circuit, the current (I) is constant through all components. The power dissipated by each bulb is given by P = I²·R. Since I² is the same for every bulb, the power (P) is directly proportional to its resistance (R). Therefore, the bulb with the higher resistance will dissipate more power and consequently shine brighter.

Question 2: When two light bulbs of different resistances are connected in a series circuit, the bulb with the lower resistance will always dissipate more power.

A. Yes

B. No

Explanation: In a series circuit, the current (I) is the same through all components. To determine power dissipation, the formula P = I²·R is used. Since the current (I²) is constant for every bulb in series, the power dissipated (P) is directly proportional to its resistance (R). Therefore, the bulb with the higher resistance will dissipate more power and shine brighter, not the one with lower resistance.

Question 3: Which of the following statements correctly describe the derivation of alternative power formulas from the fundamental power formula P = U·I, using Ohm's Law?

A. Substituting U = I·R into P = U·I leads to P = I²·R.

B. Substituting I = U/R into P = U·I leads to P = U²/R.

C. Substituting R = U/I into P = U·I leads to P = U²/R.

D. Substituting U = P/I into P = U·I leads to P = I²·R.

Explanation: The study material states two main derivations: 1. Substitute U = I·R into P = U·I to get P = (I·R)·I = I²·R. This matches option 0. 2. Substitute I = U/R into P = U·I to get P = U·(U/R) = U²/R. This matches option 1. Option 2 describes substituting R=U/I, which is correct, but then incorrectly states it leads to P = U²/R. If R=U/I is substituted, it would be P = U·I. To get U²/R, I=U/R is substituted. Option 3 presents an incorrect substitution for U (P/I is derived from P=U·I, not part of Ohm's law for this derivation) to derive I²·R.

Question 4: Which of the following statements accurately describe the characteristics of a series circuit?

A. The total resistance is the sum of the individual resistances of all components.

B. The voltage across each component is the same.

C. The current is the same through all components.

D. Components are connected across the same two points, providing multiple paths for current.

Explanation: In a series circuit, the total resistance is indeed the sum of the individual resistances (R_total = R₁ + R₂ + ...). Also, the current is the same through all components (I_total = I₁ = I₂ = ...). The voltage divides across components, meaning the voltage across each component is generally different and only the sum equals the total voltage (U_total = U₁ + U₂ + ...). Components connected across the same two points with multiple paths for current describe a parallel circuit, not a series circuit.

Question 5: In a series circuit, the power formula P = I²·R is considered relevant because the current (I) is constant throughout the circuit.

A. Yes

B. No

Explanation: The study materials state under 'Series Brightness Challenge', Step 3: 'In a series circuit, current (I) is constant. Therefore, P = I²·R is the relevant formula.'