An electric bulb is connected to a 110 V generator. The current is 0.2 A. What is the power of the bulb ?
22 W
This question asks us to calculate the power of an electric bulb given the voltage across it and the current flowing through it. To find the electric power, we need to use the fundamental relationship between power, voltage, and current in an electrical circuit.
Understanding Electric Power
Electric power is the rate at which electrical energy is transferred by an electric circuit. It is a measure of how much work is done by the electric current per unit of time. The standard unit of electric power is the Watt (W).
Formula for Electric Power
The power (P) dissipated by an electrical device, such as an electric bulb, is related to the voltage (V) across it and the current (I) flowing through it by the following formula:
\[P = V \times I\]
Where:
- P is the electric power in Watts (W)
- V is the voltage in Volts (V)
- I is the current in Amperes (A)
Applying the Formula to the Electric Bulb Problem
We are given the following information about the electric bulb:
- Voltage (V) = 110 V
- Current (I) = 0.2 A
Now, we can substitute these values into the formula for electric power:
\[P = V \times I\]
\[P = 110 \text{ V} \times 0.2 \text{ A}\]
\[P = 22 \text{ W}\]
So, the power of the electric bulb is 22 Watts.
Step-by-Step Calculation
Let's break down the calculation:
- Identify the given values: Voltage (V) and Current (I).
- Recall the formula for power: P = V \(\times\) I.
- Substitute the given values into the formula: P = 110 V \(\times\) 0.2 A.
- Perform the multiplication: 110 \(\times\) 0.2 = 22.
- State the result with the correct unit: P = 22 W.
Verifying the Answer Options
Let's compare our calculated power of 22 W with the given options:
- Option 1: 0.22 W (Incorrect)
- Option 2: 2.2 W (Incorrect)
- Option 3: 22 W (Correct)
- Option 4: 220 W (Incorrect)
Our calculated value of 22 W matches Option 3.
| Quantity | Symbol | Given Value | Unit |
|---|---|---|---|
| Voltage | V | 110 | V |
| Current | I | 0.2 | A |
| Power | P | ? | W |
Revision Table: Electric Power Concepts
| Concept | Formula | Units | Explanation |
|---|---|---|---|
| Electric Power | P = V \(\times\) I | Watts (W) | Rate of energy transfer in an electric circuit. |
| Voltage | V | Volts (V) | Electric potential difference across components. |
| Current | I | Amperes (A) | Rate of flow of electric charge. |
| Energy | E = P \(\times\) t | Joules (J) or Watt-hours (Wh) | Power multiplied by time. |
Additional Information on Electric Power Calculation
Besides P = V \(\times\) I, electric power can also be calculated using Ohm's Law, which states V = I \(\times\) R (where R is resistance). By substituting Ohm's Law into the power formula, we get alternative formulas:
- Substituting V = I \(\times\) R into P = V \(\times\) I gives: P = (I \(\times\) R) \(\times\) I = \[P = I^2 R\]
- Substituting I = V / R into P = V \(\times\) I gives: P = V \(\times\) (V / R) = \[P = \frac{V^2}{R}\]
These formulas can be used to calculate electric power if voltage and resistance, or current and resistance, are known instead of voltage and current. In this specific problem involving the electric bulb, we were given voltage and current, making the P = V \(\times\) I formula the most direct approach.
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