Chapter 26, Problem Q26.1DQ

In which 120-V light bulb does the filament have greater resistance: a 60-W bulb or a 120-W bulb? If the two bulbs are connected to a 120-V line in series, through which bulb will there be the greater voltage drop? What if they are connected in parallel? Explain your reasoning.

To determine

The greater resistance of the $60\text{W}$ and $120\text{W}$ bulb with the voltage source of $120\text{V}$, the greater voltage drop of the bulb when the bulb connected in series and parallel.

Answer to Problem Q26.1DQ

The $60\text{W}$ bulb has the greater resistance, the $60\text{W}$ has the greater voltage drop when the bulbs are connected in series, and both bulbs have the same voltage drop when the bulbs are connected in parallel.

Explanation of Solution

Case 1:

To determine: Whether the greater resistance has the $60\text{W}$ bulb or $120\text{W}$ bulb with the voltage source of $120\text{V}$.

Introduction: The power of the bulb increases, as the resistance decreases.

Formula to calculate the power delivered by the bulb is,

  $P=\frac{V^2}{R}$                                                                                                          (I)

• $V$ is the voltage across the bulb,
• $R$ is the resistance of the bulb.

From equation (I), the power delivered to the bulb is inversely proportional to the resistance of the bulb.

Therefore, when the resistance of the bulb increases the power decreases and the power of the bulb increases ,when the resistance of the bulb decreases.

Thus, $60\text{W}$ bulb has the greater resistance.

Case 2:

To determine: The greater voltage drop of the bulbs when the bulbs are connected in series.

Introduction: If the bulbs are connected in series the voltage drop depends on the value of resistance, if the resistance increases the voltage drop increases.

When the bulbs are connected in series the current through each of the bulb in the circuit is same.

Formula to calculate the voltage across the resistor using Ohm’s law is,

  $V=IR$                                                                                                        (II)

• $V$ is the voltage across the resistor,
• $R$ is the resistance.

From equation (II), the voltage drop across the resistor and its resistance value is directly proportional.

Therefore, when the resistance of the bulb decreases, the voltage across the bulb decreases and the voltage across the bulb of the bulb increases, when the resistance of the bulb increases.

From case 1, the $60\text{W}$ bulb has the greater resistance, therefore $60\text{W}$ bulb has the greater voltage drop when the bulbs are connected in series.

Thus, the $60\text{W}$ bulb has the greater voltage drop.

Case 3:

To determine: The greater voltage drop of the bulbs when the bulbs are connected in parallel.

Introduction: If the circuit elements are connected in parallel the voltage drop across each element is same.

When the bulbs are connected in parallel the voltage drop across each in the parallel circuit is same

Thus, both bulbs have the same voltage drop.

Conclusion:

Therefore, the $60\text{W}$ bulb has the greater resistance, the $60\text{W}$ has the greater voltage drop when the bulbs are connected in series, and both bulbs have the same voltage drop when the bulbs are connected in parallel.