a 75w and 50 w incandescent light bulbs are designed fot use with the same voltage. what is the ratio of the resistance of the 75- w bulb to the resistance of the 50 w bulb?
power= v^2/R
so power is inverely prop to resistance.
R75/R50=50/75
0.67
To find the ratio of resistance between two light bulbs, we can use the equation P = V^2/R, where P represents power, V represents voltage, and R represents resistance.
Given that the light bulbs are designed for use with the same voltage, we can assume that the voltage (V) is constant for both bulbs. Let's assign it a variable, say V.
Let's consider the 75-watt bulb first. According to the equation P = V^2/R, we know the power (P) is 75 watts. Plugging these values into the equation, we get:
75 = V^2 / R1
Now, let's consider the 50-watt bulb. Again, using the equation P = V^2/R, and with the power (P) equal to 50 watts, we get:
50 = V^2 / R2
We want to find the ratio of resistance, so we want to compare R1 and R2. To do that, let's rearrange the equations:
V^2 = 75 * R1 --> Equation 1
V^2 = 50 * R2 --> Equation 2
Now, we can set the two equations equal to each other to find the ratio:
75 * R1 = 50 * R2
To find the ratio of resistance between the two bulbs, divide the resistance of the 75W bulb (R1) by the resistance of the 50W bulb (R2). So, the ratio is:
R1/R2 = (75/50)
Simplifying the fraction, we get:
R1/R2 = 3/2
Therefore, the ratio of resistance of the 75W bulb to the 50W bulb is 3:2.