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How many incandescent lamps connected in series would consume the same total power as a single 100 W/220 V incandescent lamp. The rating of each lamp is 200 W/220 V?
- a)Not possible
- b)4
- c)3
- d)2
Correct answer is option 'D'. Can you explain this answer?
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How many incandescent lamps connected in series would consume the same...
To determine the number of incandescent lamps connected in series that would consume the same total power as a single 100 W/220 V incandescent lamp with each lamp rated at 200 W/220 V, we need to calculate the total power consumed by the series combination of lamps.
Let's assume the number of lamps connected in series is 'n'.
Total power consumed by the series combination of lamps can be calculated using the formula:
Total Power = Power per Lamp * Number of Lamps
Given that the power per lamp is 200 W and the voltage is 220 V, we can determine the current flowing through each lamp using Ohm's law:
Current per Lamp = Power per Lamp / Voltage per Lamp
Substituting the values, we get:
Current per Lamp = 200 W / 220 V = 0.909 A
Since the lamps are connected in series, the total current flowing through the combination will be the same as the current flowing through each lamp.
Total Current = Current per Lamp = 0.909 A
Now, let's calculate the total power consumed by the series combination of lamps:
Total Power = Power per Lamp * Number of Lamps
100 W = 200 W * n
Solving for 'n', we get:
n = 100 W / 200 W = 0.5
Since 'n' cannot be a fraction, we round it up to the nearest whole number, which is 1.
Therefore, the number of incandescent lamps connected in series that would consume the same total power as a single 100 W/220 V incandescent lamp is 1.
However, none of the given options match the correct answer. Option 'D' cannot be the correct answer. It seems there may be an error in the options provided.
Let's assume the number of lamps connected in series is 'n'.
Total power consumed by the series combination of lamps can be calculated using the formula:
Total Power = Power per Lamp * Number of Lamps
Given that the power per lamp is 200 W and the voltage is 220 V, we can determine the current flowing through each lamp using Ohm's law:
Current per Lamp = Power per Lamp / Voltage per Lamp
Substituting the values, we get:
Current per Lamp = 200 W / 220 V = 0.909 A
Since the lamps are connected in series, the total current flowing through the combination will be the same as the current flowing through each lamp.
Total Current = Current per Lamp = 0.909 A
Now, let's calculate the total power consumed by the series combination of lamps:
Total Power = Power per Lamp * Number of Lamps
100 W = 200 W * n
Solving for 'n', we get:
n = 100 W / 200 W = 0.5
Since 'n' cannot be a fraction, we round it up to the nearest whole number, which is 1.
Therefore, the number of incandescent lamps connected in series that would consume the same total power as a single 100 W/220 V incandescent lamp is 1.
However, none of the given options match the correct answer. Option 'D' cannot be the correct answer. It seems there may be an error in the options provided.
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How many incandescent lamps connected in series would consume the same...
In series power = 1/p
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