Problem 20 - Applied Physics

Question

A transformer has an output power of \(990 \mathrm{~W}\). If the current in the secondary coil is \(0.45 \mathrm{~A}\), what is its voltage?

Step-by-Step Solution

Answer

The voltage is 2200 V.

Step 1: Identify the Given Values

We are given two key pieces of information: the output power of the transformer, which is \(990 \mathrm{~W}\), and the current in the secondary coil, which is \(0.45 \mathrm{~A}\). Our goal is to find the voltage across the secondary coil.

Step 2: Use the Power Formula

The relationship between power (\(P\)), current (\(I\)), and voltage (\(V\)) is given by the formula \(P = IV\). This formula allows us to calculate the voltage if we know the power and the current.

Step 3: Rearrange the Power Formula

We can rearrange the formula \(P = IV\) to solve for voltage \(V\). By dividing both sides of the equation by the current \(I\), we have:\[V = \frac{P}{I}\]

Step 4: Substitute the Known Values

Now, substitute the known values of power and current into the equation. We have \(P = 990 \mathrm{~W}\) and \(I = 0.45 \mathrm{~A}\):\[V = \frac{990 \mathrm{~W}}{0.45 \mathrm{~A}}\]

Step 5: Calculate the Voltage

Perform the division to find the voltage:\[V = \frac{990}{0.45} = 2200 \mathrm{~V}\]

Step 6: Conclusion

The voltage across the secondary coil of the transformer is \(2200 \mathrm{~V}\).

Key Concepts

Power Formula in Physics

In physics, power is a fundamental concept that describes the rate at which energy is transferred or converted. Power is measured in watts (W) and is calculated using the formula \( P = IV \). Here, \( P \) represents power, \( I \) is the current in amperes (A), and \( V \) is the voltage in volts (V). This formula is particularly useful for understanding electrical systems, such as transformers, because it relates the power to the flow of electrical current and the voltage across a system.

To understand this formula:

• The relationship indicates that power increases with an increase in current or voltage.
• If you know any two of the variables, you can calculate the third.
• This relationship is fundamental for designing circuits and electrical systems.

In the context of the transformer, knowing the power and current allows us to find the missing voltage, ensuring the transformer operates efficiently.

Current and Voltage Relationship

Current and voltage have a direct relationship that is crucial in understanding and working with electrical components and systems. Current refers to the flow of electric charge, while voltage is the potential difference that pushes the charge through a circuit. Together, they form a continuous flow, allowing devices to operate.

To grasp their relationship:

• Voltage is likened to the pressure that forces water through a hose, while current is the flow of water.
• The greater the voltage, the higher the potential for current to flow through a given resistance within a circuit.
• This relationship is dictated by Ohm's Law, which states \( V = IR \), where \( R \) is resistance.

In transformers, handling these values accurately is crucial, as incorrect assumptions can affect performance and cause inefficiencies.

Electrical Calculations

Electrical calculations are essential for determining various parameters in any electrical system. They guide the design, operation, and troubleshooting of electrical appliances and systems. Understanding how to carry out these calculations ensures safety and efficiency in handling electrical systems.

When performing electrical calculations:

• Begin by identifying known values like power, current, or voltage.
• Use foundational formulas, such as the power formula \( P = IV \), to solve for missing elements.
• Substitute known values carefully to avoid errors, particularly in complex systems.

In the case of the transformer problem, starting with the power formula allows for precise calculation of the voltage when given the power and current, leading to the accurate result of 2200 volts. These calculations are vital for ensuring electrical systems function optimally and safely.