A 346 W bulb and a 173 W bulb are both
designed to operate at standard household
voltage of 120 V.
Determine which bulb has the lower filament resistance and then calculate the value
of its resistance.
Answer in units of Ω
To determine which bulb has the lower filament resistance, we can use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I).
We know that the power (P) of a bulb can be calculated as the product of voltage and current (P = V * I).
For the 346 W bulb:
P = 346 W
V = 120 V
Using the power formula, we can rearrange it to solve for current:
P = V * I
346 W = 120 V * I
I = 346 W / 120 V
I ≈ 2.883 A
Now we can use Ohm's Law to calculate the resistance of the 346 W bulb:
R = V / I
R = 120 V / 2.883 A
R ≈ 41.61 Ω
For the 173 W bulb:
P = 173 W
V = 120 V
Again, using the power formula to solve for current:
173 W = 120 V * I
I = 173 W / 120 V
I ≈ 1.442 A
Calculating the resistance using Ohm's Law for the 173 W bulb:
R = V / I
R = 120 V / 1.442 A
R ≈ 83.16 Ω
From the calculations, we can determine that the 346 W bulb has the lower filament resistance, with a value of approximately 41.61 Ω.
To determine which bulb has the lower filament resistance, we can use the formula for power:
P = V^2 / R
where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms.
For the 346 W bulb, we know the power is 346 W and the voltage is 120 V. We can rearrange the formula to solve for R:
R = V^2 / P
Plugging in the values:
R = (120^2) / 346
Calculating this, we find that the resistance of the 346 W bulb is approximately 41.6 ohms.
For the 173 W bulb, we can repeat the same process. Plugging in the values:
R = (120^2) / 173
Calculating this, we find that the resistance of the 173 W bulb is approximately 82.9 ohms.
Comparing the two resistances, we can see that the 346 W bulb has the lower filament resistance at 41.6 ohms.