We have given two lamps in such a way :
Power of 1st lamp, P₁ = 40W , voltage of 1st lamp, V₁ = 220V
power of 2nd lamp , P₂ = 60W , voltage of 2nd lamp ,V₂ = 220V

we know, one things ,
Power = V²/R [ when potential difference is same then consider P = V²/R ]
R = V²/P
so, resistance of 1st lamp , R₁ = V₁²/P₁ = (220)²/60 = 4840/6 = 2420/3Ω
resistance of 2nd lamp , R₂ = V₂²/P₂ = (220)²/40 = 48400/40 = 1210Ω
Now, question said ,
(a) Both the lamps are in parallel ,
So, 1/Req = 1/R₁ + 1/R₂
1/Req = 3/2420 + 1/1210 = 5/2420 = 1/484
Req = 484Ω

Now, Current drawn from electrical supply ,i = potential difference/Req
= 220V/484 = 20/44 = 5/11 A

(b) energy consumed by lamps in one hour = Energy consumed by 1st lamps in one hour + energy consumed by 2nd lamps in one hour
= P₁ × 1hour + P₂ × 1 hour
=(P₁ + P₂) × 1 hour
= (60W + 40W) × 1 hour
= 100 Wh
= 100/1000 KWh [ ∵ 1 KWh = 10²Wh ]
= 0.1 KWh

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Calculation of Current Drawn from the Line:

To calculate the current drawn from the line, we need to use Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance.

Formula:
Current (I) = Voltage (V) / Resistance (R)

Given Data:
Lamp 1: Power (P1) = 100 watts, Voltage (V) = 220 volts
Lamp 2: Power (P2) = 60 watts, Voltage (V) = 220 volts

Calculating Resistance:
Resistance (R) can be calculated using the formula:
Resistance (R) = (Voltage (V))^2 / Power (P)

For Lamp 1:
Resistance (R1) = (220 volts)^2 / 100 watts
Resistance (R1) = 48400 / 100
Resistance (R1) = 484 ohms

For Lamp 2:
Resistance (R2) = (220 volts)^2 / 60 watts
Resistance (R2) = 48400 / 60
Resistance (R2) = 806.67 ohms

Calculating Total Resistance:
Since the lamps are connected in parallel, the total resistance (Rt) can be calculated using the formula:
1/Rt = 1/R1 + 1/R2

1/Rt = 1/484 + 1/806.67
1/Rt = 0.00207 + 0.00124
1/Rt = 0.00331

Rt = 1 / 0.00331
Rt = 301.81 ohms

Calculating Current:
Now, we can calculate the current (I) by substituting the values into the formula:
Current (I) = Voltage (V) / Resistance (Rt)

Current (I) = 220 volts / 301.81 ohms
Current (I) = 0.7298 Amps (approximately)

Therefore, the current drawn from the line when the supply voltage is 220 volts is approximately 0.7298 Amps.

Explanation:
When two lamps are connected in parallel, they receive the same voltage across them. The current flowing through each lamp is determined by its resistance. In this case, Lamp 1 has a higher power rating, which means it has a lower resistance compared to Lamp 2. As a result, Lamp 1 draws more current than Lamp 2. When connected in parallel, the total resistance of the circuit decreases, which allows a higher current to flow from the mains supply. The total current drawn from the line is the sum of the individual currents drawn by each lamp.