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In transformers, the turns ratio is a crucial concept and determines how the voltages are transformed from one side to the other. The turns ratio is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil. This ratio dictates how the input voltage is stepped-up or stepped-down to meet the required output voltage level. For example, if you have a transformer connected to a wall socket with 120 V, and the equipment (like a laptop battery) requires only 9 V, the turns ratio helps adjust the voltage to a suitable level. You calculate it using the formula:

• Turns Ratio (n) = \(\frac{V_{\text{input}}}{V_{\text{output}}}\)

When you insert the necessary values:

• \(n = \frac{120\, \text{V}}{9.0\, \text{V}}\)

You’ll find that the turns ratio is approximately 13.33. This means the primary coil has 13.33 times more turns than the secondary coil to achieve the required voltage reduction.

The current from the wall socket, or the input current (\(I_{\text{primary}}\)), can be determined by understanding the conservation of power in transformers. Despite some power loss in practical applications, transformers ideally ensure that power in the primary circuit equals the power in the secondary circuit, granted the assumption of no losses: \(P_{\text{primary}} = P_{\text{secondary}}\).To calculate the input current, remember the relationship:

• \(V_{\text{input}} \times I_{\text{primary}} = V_{\text{output}} \times I_{\text{output}}\)

Solving for the primary current:

• \(I_{\text{primary}} = \frac{V_{\text{output}} \times I_{\text{output}}}{V_{\text{input}}}\)

Substitute the known values of 9.0 V and 225 mA:

• \(I_{\text{primary}} = \frac{9.0\, \text{V} \times 0.225\, \text{A}}{120\, \text{V}}\)

This calculation shows that the current coming from the wall socket is approximately 16.9 mA. Knowing this current is important for managing energy efficiency and ensuring safety when designing or using electronic devices.

The power delivered through the transformer from the wall socket is a measurement of how effectively energy is transmitted from the primary side to the secondary side. It involves calculating the total energy per unit time delivered to the primary and secondary circuits.The power delivered by the wall socket, represented as primary power \(P_{\text{primary}}\), uses the equation:

• \(P_{\text{primary}} = V_{\text{input}} \times I_{\text{primary}}\)

By inserting the values:

• \(P_{\text{primary}} = 120\, \text{V} \times 0.0169\, \text{A} \approx 2.028\, \text{W}\)

Similarly, the power used by the batteries, or the secondary power \(P_{\text{secondary}}\), is calculated as:

• \(P_{\text{secondary}} = V_{\text{output}} \times I_{\text{output}}\)
• \(P_{\text{secondary}} = 9.0\, \text{V} \times 0.225\, \text{A} = 2.025\, \text{W}\)

Understanding both ends of power usage gives insights on the efficiency and effectiveness of the transformer in serving its purpose while minimizing energy waste. This knowledge helps in optimizing performance and ensuring devices function within safe and reliable electrical parameters.