Find the circuit current for the following loads connected in a building if supply voltages are 230 V AC: a. 4 lamps each of 500 W b. 4 fans each of 100 W c. 1 TV of 200 W
11.3 A
Calculating Circuit Current for Building Loads
To find the total circuit current for multiple loads connected in a building, we first need to calculate the total power consumed by all the loads. Then, we can use the relationship between power, voltage, and current.
The loads given are:
- 4 lamps, each of 500 W
- 4 fans, each of 100 W
- 1 TV of 200 W
Let's calculate the total power for each type of load:
- Total power of lamps = Number of lamps \(\times\) Power per lamp
- Total power of lamps = 4 \(\times\) 500 W = 2000 W
- Total power of fans = Number of fans \(\times\) Power per fan
- Total power of fans = 4 \(\times\) 100 W = 400 W
- Total power of TV = 1 \(\times\) 200 W = 200 W
Now, let's find the total power consumed by all loads:
Total Power (\(P_{total}\)) = Power of lamps + Power of fans + Power of TV
\(P_{total}\) = 2000 W + 400 W + 200 W = 2600 W
The supply voltage (\(V\)) is given as 230 V AC.
The relationship between power (P), voltage (V), and current (I) in an AC circuit is given by:
\(P = V \times I \times \cos(\phi)\)
For resistive loads like lamps and heating elements, the power factor \(\cos(\phi)\) is approximately 1. For loads like fans and TVs which contain inductive components, the power factor is typically less than 1. However, when calculating the total current based on the total apparent power (which is close to the total real power for typical household loads without significant phase difference being specified), we often use the simplified formula \(P = V \times I\) for an approximate calculation, especially when the power factor is not provided for individual loads or for the total circuit.
Using the simplified formula \(I = P / V\):
Circuit Current (I) = Total Power (\(P_{total}\)) / Supply Voltage (\(V\))
Let's calculate the current:
\(I = \frac{2600 \text{ W}}{230 \text{ V}}\)
\(I \approx 11.304 \text{ A}\)
Comparing this value with the given options, the closest value is 11.3 A.
Therefore, the circuit current is approximately 11.3 A.
| Load Type | Quantity | Power per unit (W) | Total Power (W) |
|---|---|---|---|
| Lamps | 4 | 500 | 4 \(\times\) 500 = 2000 |
| Fans | 4 | 100 | 4 \(\times\) 100 = 400 |
| TV | 1 | 200 | 1 \(\times\) 200 = 200 |
| Total Power (\(P_{total}\)) | 2600 W |
Using the formula \(I = \frac{P_{total}}{V}\):
\[ I = \frac{2600 \text{ W}}{230 \text{ V}} \] \[ I \approx 11.304 \text{ A} \]Rounding to one decimal place, the current is approximately 11.3 A.
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