three lamps connected to a 120-V AC (rms) household supply voltage. Lamps 1 and 2 have 75.0-W bulbs; lamp 3 has a 40.0-W bulb.
(a) For each bulb, find the rms current.
Irms, lamp 1 = A
Irms, lamp 2 = A
Irms, lamp 3 = A
(b) For each bulb, find the resistance.
Rlamp 1 = Ω
Rlamp 2 = Ω
Rlamp 3 = Ω
The lamps are in parallel and all have an applied voltage of 120 V (rms)
(a) Irms = P/V
where P is the lamp power rating in Watts.
(b) V^2/R = P for each lamp
R = V^2/P = 1.44*10^4/P ohms
To find the rms current for each bulb, we can use Ohm's Law, which states that the current (I) flowing through a device is equal to the voltage (V) across it divided by the resistance (R) of the device. The equation is given by:
I = V / R
a) For Lamp 1:
The power (P) of the bulb is given as 75.0 W. Since power is defined as the product of voltage and current (P = V * I), we can rearrange this equation to solve for current:
I = P / V
Substituting the values, we get:
I1 = 75.0 W / 120 V
Using a calculator:
I1 = 0.625 A
Therefore, Irms, lamp 1 = 0.625 A.
b) To find the resistance of each lamp, we can rearrange the power equation to solve for resistance:
R = V^2 / P
b) For Lamp 1:
Substituting the given values:
R1 = (120 V)^2 / 75.0 W
Using a calculator:
R1 = 192 Ω
Therefore, Rlamp 1 = 192 Ω.
Repeating the same steps for Lamp 2 and Lamp 3, we can find their respective rms currents and resistances.