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