two lamps one rated 100w , 220v and 10w at 220v are connected in parallel to 220v supply. calculate the total current through the circuit.
Answers
Power = P = 100 W
Voltage = V = 220v
Resistance = R
P = V²/R
100 = 220 ×220/R
R = 220 × 220/100
= 484 Ω
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Power = P = 10 W
Voltage = V = 220v
Resistance = R
P = V²/R
10 = 220 × 220/R
R = 220× 220/10
=4840 Ω
=========================
As the resistors are connected in parallel ,
total resistance = 1/R
1/R = 1/484 + 1/4840
= 4840 + 484/484×4840
= 5324/2342560
R = 2342560/5324 = 440 ohms
Total resistance = 440 Ω
I = current
V = IR
220 = I × 440
I = 220/440
= 0.5 A
The current drawn is 0.5 A
The total current through the circuit is 0.5 A.
Explanation:
Given:
Power of 1st lamp= 100W
Voltage of 1st lamp= 220v
Power of 2nd lamp= 10W
Voltage of 2nd lamp= 220v
Total current through circuit= ?
Resistance = R
P = V²/R (1st lamp)
100 = 220 ×220/R
R = 220 × 220/100
R = 484 Ω
Similarly for second lamp,
P = V²/R (2nd lamp)
10 = 220 × 220/R
R = 220× 220/10
R =4840 Ω
Since the resistors are connected parallel,
Total resistance = 1/R
1/R = 1/484 + 1/4840
= 4840 + 484/484×4840
= 5324/2342560
R = 2342560/5324 = 440 ohms
Total resistance = 440 Ω
To identify the total current through the circuit
V = IR
220 = I × 440
I = 220/440
I = 0.5 A
The total current through the circuit is 0.5 A.
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