A 75-W, 120-V bulb is connected in parallel with 25-W, 120-V bulb. What is the net resistance?
P = 75 + 25 = 100 W., Total.
P = 120 * I = 100
I = 100/120 = 0.833A
R = E/I = 120/0.83333 = 144 Ohms.
To calculate the net resistance in a parallel circuit, you need to know the power and voltage ratings of each bulb. Fortunately, you already have this information.
First, we need to determine the resistance of each bulb. We can use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by power (P).
For the 75-W bulb:
Resistance (R1) = V1 / P1 = 120 V / 75 W = 1.6 ohms
For the 25-W bulb:
Resistance (R2) = V2 / P2 = 120 V / 25 W = 4.8 ohms
Next, we can calculate the total resistance (Rt) of the parallel circuit. In a parallel circuit, the total resistance is given by the reciprocal of the sum of the reciprocals of the individual resistances.
1 / Rt = 1 / R1 + 1 / R2
1 / Rt = 1 / 1.6 + 1 / 4.8
Let's simplify this expression:
1 / Rt = 3/4 + 1/4
1 / Rt = 4/4
1 / Rt = 1
To find Rt, take the reciprocal of both sides:
Rt = 1 ohm
Therefore, the net resistance of the circuit is 1 ohm.