A current $\text{i}_1=\text{i}_0\sin\omega\text{t}$ passes through a resistor of resistance $R.$ How much thermal energy is produced in one time period? A current $\text{i}_2=-\text{i}_0\sin\omega\text{t}$ passes through the resistor. How much thermal energy is produced in one time period? If $i_1,$ and $i_2$ both pass through the resistor simultaneously, how much thermal energy is produced? Is the principle of superposition obeyed in this case?
Answer
$\text{I}_\text{rms}^{2}\times\text{R}\times\frac{2\pi}{\omega}$ from definition of $\text{rms}$ current.
$i_1,$ and $i_2$ both pass through the resistor simultaneously, and same thermal energy is produced.
Similary, the principle of superposition obeyed in this case zero.
An $AC$ source is connected to a capacitor. Will the rms current increase, decrease or remain constant if a dielectric slab is inserted into the capacitor?
Answer
$\text{X}_\text{c}=\frac{1}{\omega\text{C}}$ as slab is introduced $C$ increases and $X_C$ decreases so current increases.
When the frequency of the AC source in an LCR circuit equals the resonant frequency, the reactance of the circuit is zero. Does it mean that there is no current through the inductor or the capacitor?
Answer
There is current but the potential difference across inductor and capacitor cancel each other.
Two alternating currents are given by, $\text{i}_\text{i}=\text{i}_0\sin\omega\text{t}$ and $\text{i}_\text{i}=\text{i}_0\sin\Big(\omega\text{t}+\frac{\pi}{3}\Big)$ Will the $\text{rms}$ values of the currents be equal or different?
Answer
$\text{I}_{\text{rms}}$ will be equal because in a complete cycle heat dissipated will be equal for both.
When an AC source is connected to a capacitor there is a steady-state current in the circuit. Does it mean thatthe charges jump from one plate to the other to complete the circuit?
