Calculating the Resistance of a Light Bulb Connected to a 110-V Source
Understanding the Relationship between Power, Voltage, and Resistance
When a light bulb is connected to a 110-V source, the power consumed by the bulb can be calculated using the formula P = IV, where P is power, I is current, and V is voltage. Additionally, according to Ohm's law, the voltage across a resistor (in this case, the light bulb) is equal to the current flowing through it multiplied by the resistance of the resistor (V = IR).
Given that the light bulb has a power rating of 100 Watts, and the source voltage is 110V, we can calculate the resistance of the light bulb.
Question:
A light bulb is connected to a 110-V source. What is the resistance of this bulb if it is a 100-W bulb?
Answer:
121 ohms
Explanation:
Formula used for calculating power P = current * voltage
P = IV
Substituting V = IR into the formula for calculating power, we get:
P = IV
P = (V/R)V
P = V²/R
Given parameters:
Power rating of the bulb P = 100 Watts
Source voltage V = 110V
Required: Resistance of the bulb R
Substituting the given parameters into the formula for calculating power:
P = V²/R
100 = 110²/R
R = 110²/100
R = 110 * 110/100
R = 12100/100
R = 121 ohms
Hence, the resistance of this bulb is 121 ohms