Question

Answer the following questions:
a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltage across the series element of the circuit? Is the same rule for RMS voltage?
b) A capacitor is used in the primary circuit of an induced coil.
c) An applied voltage has a superposition of an ac as well as dc signal in a circuit having capacitor and inductor. Show that the ac signal is shown across the inductor and dc across the capacitor.
d) A choke coil in series with a lamp is connected with a dc line; the lamp is made to shine brightly. The insertion of an iron rod in the choke coil, made no changes in the brightness of the lamp. Predict the corresponding connection made with an ac line.
e) Why choke coil is needed to be used in the fluorescent tube made with ac mains? Why cannot we use an ordinary resistor instead of choke coil?

Answer 1

We have the following proved reasons to solve the given question. Ohm’s law, KCL and KVL are always obeyed by any ac or dc circuit. Capacitors show transient behaviour when connected with ac or dc circuits. Choke produces very high initial voltage. Capacitor resists the spark production when used in induced coil’s circuit.

Complete step by step solution:
a) Yes, in any ac circuit instantaneous voltage is equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit, as instantaneous voltages are in the same phase always and quantities in the same can be added. RMS values of the voltages have different phase values so they cannot be added and hence cannot have an algebraic sum equal to the main voltage.

b) Capacitor is used in the primary circuit of the induction coil because when the circuit breaks down high voltage flows through the circuit if capacitor will be present that extra voltage will be used up in charging the capacitor and likewise no sparking takes place.

c) When capacitor and inductor are present in the circuit and receive superposition of ac or dc signal, capacitor has ${X_c} = \dfrac{1}{{j\omega C}}$ in dc signal $\omega$ will be zero therefore ${X_c}$ will be infinite. Thus, it receives a dc signal. Similarly, for inductor${X_L} = j\omega L$, in ac signal $\omega$ will be high thus, inductor receives ac signal.

d) A choke coil connected in an ac line, is inserted with an iron rod dims the lamp light because insertion of iron rod further increases the impedance of the entire circuit and allows less current to flow which reduces the brightness of the lamp.

e) Choke coil gives initially high voltage to let the fluorescent tube to light as the tube grows to full choke coil reduces the voltage without any energy losses because average power in an inductor is zero. If a resistor would be used in place of choke coil loss of energy would take place as heat dissipation.

Note: When a capacitor is placed in series with a resistor initially having zero charge and is not supplied by a voltage source, the capacitor will act as short circuit by the time when supply is given the capacitor current becomes zero and it will act as an open circuit.