Non-Sinusoidal Waveforms

Problem 310: The total current in a given circuit has the equation: i = 10 + 16 sinwt - 8 sin2wt + 5 cos3wt. Calculate the effective value of the current.

Problem 311: Determine rms value of the current drawn by a 2 \(\mu F\) condenser, which is connected across a source of potential. The potential has a third and fifth harmonic components, which are 30% and 20% respectively of the fundamental sinusoidal component. The fundamental sinusoidal component has a peak value of 1000 volts and 60 Hz frequency.

Problem 312: A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sinwt + 80 sin (3wt + 60°). Assume w = 314 radians/sec. Determine the rms value of the total current.

Problem 313: Determine the effective value of the circuit current of an emf of 151 sin 377t is connected in series with a DC emf of 110 volts. Both supply a load of 10 + j8 ohms.

Problem 314: An alternating current and a direct current flows simultaneously in the same conductor. If the effective value of the alternating current is 5 A and the direct current is 10 A, what will an AC ammeter read when connected in the circuit?

Problem 315: A 100\(\angle0^\circ\) V 120 Hz generator and a 80\(\angle0^\circ\) V 60 Hz generator are connected in series with a 60 V battery and a coil. The resistance and inductance of the coil are 3 \(\Omega\) and 2.65 mH, respectively. Determine the rms current of the coil.

Problem 316: If e = 100 sin (wt +30°) - 50 cos 3wt + 25 sin (5wt +150°) and i = 20 sin (wt+ 40°) + 10 sin (3wt +30°) - 5 sin (5wt - 50°). Calculate the power in watts.

Problem 317: Find the average power in a resistance R = 10 ohms, if the current in the Fourier-series form is i = 12 sinwt + 8 sin3wt + 3 sin5wt amperes.

Problem 318: A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sinwt + 80 sin (3wt + 60°). Assume w = 314 radians per sec. Determine the power dissipated.

Problem 319: A series RL circuit in which R = 5 \(\Omega\) and L = 20 mH has an applied voltage e = 100 + 50 sin wt + 25 sin 3wt, with w = 500 radians per sec. Determine the power dissipated in the resistor of the circuit.

Problem 320: Three sinusoidal generators and a battery are connected in series with a coil whose resistance and inductance are 8 \(\Omega\) and 26.53 mH, respectively. The frequency and rms voltages of the respective generators are 15 V, 20 Hz; 30 V, 60 Hz and 40 V, 100 Hz. The open circuit of the battery is 6 V. Neglect internal resistance of the battery. Find the apparent power delivered by the circuit.

Problem 321: A series circuit containing a 295 \(\mu F\) capacitor and a coil whose resistance and inductance are 3 \(\Omega\) and 4.42 mH, respectively are supplied by the following series connected generators: 35 V at 60 Hz, 10 V at 180 Hz and 8 V at 240 Hz. Determine the power factor of the circuit.

Problem 322: A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms. The combination is further connected in series with an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sinwt + 80 sin (3wt + 60°). Assume w = 314 radians per sec. Determine the circuit power factor.