(Solved): 1.1 A capacitor and a coil are connected in series across a 50Hz variable ac supply of 234.651 ...

1.1 A capacitor and a coil are connected in series across a $50\mathrm{Hz}$ variable ac supply of $234.65?15.51^0\mathrm{V}$. A voltage drop of $v_{\mathrm{L}}(\mathrm{t})=360\sin \left(?\mathrm{t}+30^{?}\right)\mathrm{V}$ is measured across the coil. The current flowing in the coil is $14.4\mathrm{A}$ at a power factor of 0.9063 . 1.1.1 Determine the current drawn from the supply. 1.1.2 Calculate the voltage drop across the capacitor. 1.1.3 Calculate the capacitance of the capacitor. 1.2 An ac voltage source is connected across a series circuit abcd consisting of a resistor between $\mathbf{a}$ and $\mathbf{b}$ of $12.6?$, a variable capacitor between $\mathbf{b}$ and $\mathbf{c}$ of $64?\mathrm{F}$ and a coil between $\mathbf{c}$ and $\mathbf{d}$ of $84\mathrm{mH}$ and a resistance of $8.4?$. The voltage measured across the circuit after $0.8932\mathrm{ms}$ is $94\mathrm{V}$ at $50\mathrm{Hz}$. 1.2.1 Calculate the current drawn from the source. 1.2.2 Calculate the voltage across each component. 1.2.3 Calculate the power factor of the circuit. 1.2.4 Draw a phasor diagram of the emf, component voltage drops and current. 1.3 Consider the series ac circuit shown below, When a current of 7.09 A flows through the circuit, the voltage drops across the various points are measured as shown. 1.3.1 Calculate the resistance and inductance of the coil ${\mathrm{Z}}_{\mathrm{Lbc}}$ 1.3.2 Calculate the total impedance of the circuit. 1.3.3 Calculate the voltage drop across the resistor $R_{cd}$ and the coil $Z_L$ bc. 1.3.4 Draw a phasor diagram of the emf and potential differences in the circuit.