Eight identical bulbs are connected in series across a 120-V line. If the current is 0.50 A, what is the power dissipated in each bulb?
The correct answer and explanation is:
To calculate the power dissipated in each bulb, we can use the power formula: P=IVP = IV
Where:
- PP is the power dissipated in a component (in watts),
- II is the current (in amperes),
- VV is the voltage across the component (in volts).
Step 1: Total Power Dissipated
Since the eight bulbs are connected in series, the same current flows through each bulb. The total voltage across the entire series circuit is given as 120 V, and the current flowing through the circuit is 0.50 A. To find the total power dissipated by the entire circuit, we use the formula for power: Ptotal=I×VtotalP_{\text{total}} = I \times V_{\text{total}}
Substituting the given values: Ptotal=0.50 A×120 V=60 WP_{\text{total}} = 0.50 \, \text{A} \times 120 \, \text{V} = 60 \, \text{W}
Step 2: Power Dissipated by Each Bulb
In a series circuit, the total power dissipated is distributed equally across all the bulbs because they are identical. Therefore, the power dissipated by each bulb is: Pbulb=Ptotalnumber of bulbsP_{\text{bulb}} = \frac{P_{\text{total}}}{\text{number of bulbs}} Pbulb=60 W8=7.5 WP_{\text{bulb}} = \frac{60 \, \text{W}}{8} = 7.5 \, \text{W}
Explanation:
In this setup, the current flowing through each bulb is the same since the bulbs are connected in series. The voltage drop across each bulb is the same fraction of the total voltage. The total power dissipated in the circuit is shared equally among the eight identical bulbs. Therefore, each bulb dissipates 7.5 W of power.
This demonstrates how power is distributed in a series circuit. The formula P=IVP = IV helps calculate the power for each individual bulb, based on the current and the voltage across it. In series circuits, the total voltage divides among the components, but the current remains constant.