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Two 100 W, 200V lamps are connected in series across a 200V supply. The total power consumed by each lamp will be watts-
- a)200
- b)25
- c)50
- d)100
Correct answer is option 'B'. Can you explain this answer?
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Calculation of Total Resistance
--------------------------
To calculate the total power consumed by each lamp, we need to first calculate the total resistance of the circuit. Since the lamps are connected in series, their resistances add up. We can use Ohm's law to calculate the resistance of each lamp:
R = V^2 / P
where R is resistance, V is voltage, and P is power.
For each lamp, we have:
R = 200^2 / 100 = 400 ohms
The total resistance of the circuit is the sum of the resistances of the two lamps:
R_total = 400 + 400 = 800 ohms
Calculation of Total Power
-----------------------
Now that we know the total resistance of the circuit, we can use Ohm's law again to calculate the total current:
I = V / R_total
I = 200 / 800 = 0.25 amps
The total power consumed by the circuit is:
P_total = V x I
P_total = 200 x 0.25 = 50 watts
Since the lamps are identical, they will each consume half of the total power:
P_lamp = P_total / 2
P_lamp = 50 / 2 = 25 watts
Therefore, the answer is option B - 25 watts.
--------------------------
To calculate the total power consumed by each lamp, we need to first calculate the total resistance of the circuit. Since the lamps are connected in series, their resistances add up. We can use Ohm's law to calculate the resistance of each lamp:
R = V^2 / P
where R is resistance, V is voltage, and P is power.
For each lamp, we have:
R = 200^2 / 100 = 400 ohms
The total resistance of the circuit is the sum of the resistances of the two lamps:
R_total = 400 + 400 = 800 ohms
Calculation of Total Power
-----------------------
Now that we know the total resistance of the circuit, we can use Ohm's law again to calculate the total current:
I = V / R_total
I = 200 / 800 = 0.25 amps
The total power consumed by the circuit is:
P_total = V x I
P_total = 200 x 0.25 = 50 watts
Since the lamps are identical, they will each consume half of the total power:
P_lamp = P_total / 2
P_lamp = 50 / 2 = 25 watts
Therefore, the answer is option B - 25 watts.
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