Ac Circuits

Step 1: Use the power formula.
The power in the primary coil is equal to the power in the secondary coil (since efficiency is 100%). Thus, for the secondary coil:
Step 2: Calculate the current in the primary coil.
Using the power equation for the primary coil: Solving for , we get .
Final Answer:

In an AC circuit, the total potential difference is the vector sum of the potential differences across the inductor and resistor. Using the Pythagorean theorem, we calculate the total potential difference.

Step 2: Conclusion.
The total potential difference across the circuit is 319V, corresponding to option (c).

For capacitors connected in series, the same charge is stored on both capacitors. The energy stored in a capacitor is given by , where is the capacitance and is the potential difference across the capacitor. We calculate the energy stored in the first capacitor.

Step 2: Conclusion.
The energy stored in the capacitor of capacitance is 1600 , corresponding to option (b).

For a parallel plate capacitor filled with two dielectric materials, the effective dielectric constant is given by the formula , considering the properties of the materials.

Step 2: Conclusion.
The correct ratio is , corresponding to option (c).

At resonance, the impedance of the circuit is minimized, and the voltage and current are in phase. When , the circuit behaves inductively, and the current lags behind the voltage.

Step 2: Conclusion.
The current lags behind the voltage when , corresponding to option (b).

Step 1: Capacitance with dielectric.
When a dielectric slab is introduced into a capacitor, the capacitance increases by a factor depending on the dielectric constant. The new capacitance is calculated based on the volume fraction of the dielectric inserted into the capacitor.

Step 2: Conclusion.
The new capacitance is , which corresponds to option (2).

The resonance condition for a series circuit is given by , where is the resonant angular frequency. Using the given values for and , we can calculate the inductance .