A 75-W, 120-V bulb is connected in parallel with 25-W, 120-V bulb. What is the net resistance?
Power = V²/r watts
so resistance for the 75W bulb
R1 = 120²/75 Ω = 192 Ω
Similarly calculate R2 for the 25W bulb.
Net resistance of two resistors in parallel
R = 1/(1/R1+1/R2)
Well, when it comes to resistance, I'd say that working with light bulbs is a bright idea! Now let's shed some light on this question.
When light bulbs are connected in parallel, their voltages are the same, so that's nothing to worry about. Now, let's calculate the resistance.
To find the resistance of each bulb, we can use Ohm's Law: Resistance = Voltage / Power.
For the 75-W bulb: Resistance = 120 V / 75 W = 1.6 ohms.
For the 25-W bulb: Resistance = 120 V / 25 W = 4.8 ohms.
When connected in parallel, the total resistance can be calculated using the formula:
1/Total Resistance = 1/Resistance1 + 1/Resistance2 + ...
So, let's crunch the numbers: 1/Total Resistance = 1/1.6 + 1/4.8.
After some calculations, you'll find that the total resistance comes out to be approximately 1.14 ohms.
So, drum roll please... the net resistance of these bulbs connected in parallel is approximately 1.14 ohms! Keep shining bright with those math skills!
To find the net resistance, we need to first find the individual resistances of the two bulbs and then calculate the equivalent resistance.
The power (P) of a bulb can be calculated using the formula: P = V^2 / R, where P is power in watts (W), V is voltage in volts (V), and R is resistance in ohms (Ω).
For the 75-W, 120-V bulb:
P1 = 75 W
V1 = 120 V
Using the formula, we can rearrange it to find the resistance of the bulb:
R1 = V1^2 / P1
R1 = 120^2 / 75
R1 = 192 Ω
For the 25-W, 120-V bulb:
P2 = 25 W
V2 = 120 V
Similarly, we can find the resistance of the second bulb:
R2 = V2^2 / P2
R2 = 120^2 / 25
R2 = 576 Ω
Since the two bulbs are connected in parallel, the total resistance (RT) is given by the formula: 1/RT = 1/R1 + 1/R2
1/RT = 1/192 + 1/576
1/RT = (576 + 192) / (192 * 576)
1/RT = 768 / 110592
1/RT = 1 / 144
Therefore, the total resistance (RT) is 144 Ω.
To find the net resistance when two resistors are connected in parallel, you can use the formula:
1/Req = 1/R1 + 1/R2 + ...
In this case, the resistors are actually light bulbs, but we can still use the formula since they have a fixed wattage and voltage.
For the first bulb, we are given its power (P1 = 75 W) and voltage (V1 = 120 V). To find its resistance (R1), we can use the formula:
P1 = V1^2 / R1
Rearranging the formula, we have:
R1 = V1^2 / P1
Substituting the values, we get:
R1 = (120 V)^2 / 75 W = 192 Ω
Similarly, for the second bulb, given its power (P2 = 25 W) and voltage (V2 = 120 V), we can calculate its resistance (R2):
R2 = (120 V)^2 / 25 W = 576 Ω
Now, we can find the net resistance (Req) by using the formula for resistors in parallel:
1/Req = 1/R1 + 1/R2
Substituting the values, we get:
1/Req = 1/192 Ω + 1/576 Ω
To simplify this, we can find a common denominator:
1/Req = (3/3)(1/192 Ω) + (1/3)(1/576 Ω)
= (3 + 1)/(3*192 Ω) + (1/3)*(1/576 Ω)
= 4/(3*192 Ω) + 1/(3*576 Ω)
= (4 + 1)/(3*192 Ω)
= 5/(3*192 Ω)
Now, we can find the reciprocal of 5/(3*192 Ω) to get the value of Req:
Req = (3*192 Ω)/5
= 1152 Ω/5
= 230.4 Ω
Therefore, the net resistance when the 75-W, 120-V bulb is connected in parallel with the 25-W, 120-V bulb is approximately 230.4 Ω.