A transformer has 800 turns in the primary coil and 40 turns in the secondary coil. a) What happens if an AC voltage of \(100 . \mathrm{V}\) is across the primary coil? b) If the initial \(A C\) current is \(5.00 \mathrm{~A}\), what is the output current? c) What happens if a DC current at \(100 .\) V flows into the primary coil? d) If the initial DC current is \(5.00 \mathrm{~A}\), what is the output current?

The transformer equation is: $$\frac{V_{primary}}{V_{secondary}} = \frac{N_{primary}}{N_{secondary}}$$, where \(V_{primary}\) and \(V_{secondary}\) are the primary and secondary coil voltages, and \(N_{primary}\) and \(N_{secondary}\) are the primary and secondary coil turns. Given \(V_{primary} = 100V\), \(N_{primary} = 800\), and \(N_{secondary} = 40\). To find the output voltage \(V_{secondary}\), we can rearrange the formula as: $$V_{secondary} = \frac{N_{secondary} * V_{primary}}{N_{primary}}$$ Plug in the values and calculate \(V_{secondary}\): $$V_{secondary} = \frac{40 * 100}{800} = 5V$$. So, when an AC voltage of 100V is across the primary coil, the output voltage across the secondary coil is 5V.

Using the principle of conservation of energy, for an ideal transformer, the power input at the primary coil is equal to the power output at the secondary coil. Power \(P = IV\), where \(I\) is the current and \(V\) is the voltage. From part a, we found the output voltage \(V_{secondary} = 5V\). Now, we are given the input current \(I_{primary} = 5A\) and need to find the output current \(I_{secondary}\). We can set up the following equation: $$V_{primary} * I_{primary} = V_{secondary} * I_{secondary}$$ Rearrange the formula to solve for \(I_{secondary}\): $$I_{secondary} = \frac{V_{primary} * I_{primary}}{V_{secondary}}$$ Plug in the values and calculate \(I_{secondary}\): $$I_{secondary} = \frac{100 * 5}{5} = 100A$$. So, when the initial AC current is 5A, the output current is 100A.

Transformers only work for AC input and not for DC input. This is because transformers depend on the changing magnetic field produced by AC current to induce a voltage in the secondary coil. In the case of DC current, the magnetic field does not change, so there will be no induced voltage in the secondary coil. Therefore, the output voltage for DC input is 0V.

As mentioned in part c, transformers do not work for DC input. Consequently, there will be no output current for DC input, so the output current for DC input is 0A.