An electric bulb is connected to 220 V generator. The current drawn is 600 mA. What is the power of the bulb?
132 W
Understanding Electric Power of a Bulb
This question asks us to calculate the power of an electric bulb given the voltage it's connected to and the current it draws. This is a fundamental concept in electricity, relating voltage, current, and power using Ohm's law and the power formula.
Analyzing the Given Information
We are provided with the following information:
- Voltage (V) across the electric bulb = 220 V
- Current (I) drawn by the electric bulb = 600 mA
- We need to find the Power (P) of the electric bulb.
Unit Conversion for Calculation
The voltage is given in Volts (V), which is the standard unit. However, the current is given in milliamperes (mA). The standard unit for current in power calculations is Amperes (A). We need to convert milliamperes to Amperes.
The conversion is:
\(1 \text{ A} = 1000 \text{ mA}\)
Therefore, to convert milliamperes to Amperes, we divide by 1000.
Current \(I = 600 \text{ mA} = \frac{600}{1000} \text{ A} = 0.6 \text{ A}\)
Now we have the values in standard units:
- Voltage (V) = 220 V
- Current (I) = 0.6 A
Calculating the Power of the Electric Bulb
The relationship between power (P), voltage (V), and current (I) in a DC circuit or for the instantaneous power in an AC circuit is given by the formula:
\(P = V \times I\)
Where:
- P is Power in Watts (W)
- V is Voltage in Volts (V)
- I is Current in Amperes (A)
Now, we can substitute the given values into the formula:
\(P = 220 \text{ V} \times 0.6 \text{ A}\)
Let's perform the multiplication:
\(P = 220 \times 0.6\)
\(P = 132 \text{ W}\)
So, the power of the electric bulb is 132 Watts.
Summary of Calculation Steps
| Step | Description | Value | Unit |
|---|---|---|---|
| 1 | Identify Voltage (V) | 220 | V |
| 2 | Identify Current (I) | 600 | mA |
| 3 | Convert Current to Amperes | \(600 / 1000 = 0.6\) | A |
| 4 | Apply Power Formula \(P = V \times I\) | \(220 \times 0.6\) | W |
| 5 | Resulting Power (P) | 132 | W |
The calculated power of the electric bulb is 132 W.
Comparing with Options
Let's compare our result with the given options:
- 132 W
- 13.2 W
- 1320 W
- 13200 W
Our calculated power, 132 W, matches the first option.
Therefore, the power of the electric bulb is 132 W.
Revision Table: Electric Power Concepts
| Concept | Symbol | Unit | Formula (related to V, I) |
|---|---|---|---|
| Voltage | V | Volt (V) | \(V = I \times R\) (Ohm's Law) |
| Current | I | Ampere (A) | \(I = V / R\) (Ohm's Law) |
| Resistance | R | Ohm (\(\Omega\)) | \(R = V / I\) (Ohm's Law) |
| Power | P | Watt (W) | \(P = V \times I\) |
Additional Information on Electric Power
Electric power is the rate at which electrical energy is transferred by an electric circuit. It represents how much work is done by the electrical energy source (like a generator) per unit of time.
- Units: The standard unit of power is the Watt (W), named after James Watt. One Watt is equal to one Joule per second (1 W = 1 J/s).
- Other Power Formulas: Besides \(P = V \times I\), power can also be calculated using Ohm's Law (\(V=IR\) and \(I=V/R\)):
- Using \(V=IR\): \(P = (IR) \times I = I^2R\)
- Using \(I=V/R\): \(P = V \times (V/R) = V^2/R\)
- Generator: A generator is a device that converts mechanical energy into electrical energy. In this problem, it provides the voltage source for the electric bulb.
- Electric Bulb: An electric bulb (incandescent type) works on the principle of heating effect of electric current. When current flows through a high-resistance filament, it heats up and emits light. The power rating of a bulb indicates how much power it consumes when operated at its rated voltage. Higher power generally means brighter light (for incandescent bulbs).
Understanding the relationship between voltage, current, and power is crucial for analyzing and designing electrical circuits and understanding the operation of electrical appliances like the electric bulb.
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