Question

Please explain this answer in 1-2 paragraphs and include physics concepts.

QUESTION:

An electrical circuit has three devices each plugged into a standard household powerpoint. Device A has a resistance of 1.0 kΩ (kiloohm), device B has a resistance of 3.0 kΩ and device C has a resistance of 6.0 kΩ.

If all three devices are turned on for 15 minutes, what will the total energy consumption of the three devices?

ANSWER:

Household Powerpoint

Device A – 1.0 kiloohm (kΩ)

Device B – 3.0 kΩ

Device C – 6.0 kΩ

All turned on for 15 minutes

Power (P) = Voltage (V) x Current (I)

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

Energy (E) = VI x time (t)

SI Units:

Power- Watts (W)

Voltage – Volts (V)

Current – Ampere (A)

Resistance – Ohm (Ω)

Energy – Joules (J)

Power (P) = Energy/Time

Multiply both sides by time

Power x Time = Energy

Energy = Power x Time  

Unknown variable is Current (I) (Ampere)

V = 230 (standard household powerpoint voltage)

R = 1/R1 + 1/R2 + 1/R3

1/R = 1/1000 + 1/3000 + 1/6000

1/R = 3/2000

R = 2000/3

R = 666.6666…

R = 666.67Ω(1 decimal place)

I = V/R

Therefore,

I = 230/666.67

= 0.345A

t = 15 minutes

= 900 seconds

Using E = VI x t

E = 230 x 0.345 x 900

E = 71,415 Joules

Therefore, the total energy consumption of all three devices when turned on for 15 minutes equals 71,415 Joules.

Answer 1

Here the mentioned answer is correct. But it is asked to mention the physics concept behind the working. Hence the explanation for that is that,

All the electrical appliances or devices in household connections are connected in the parallel combination. Because in parallel combination, if one device is off other devices can continue to work or will be in ON state. But where as in series it is not possible. Hence parallel combination of resistors is considered in the problem. Rest of the answer is given already.