Question

In a series R-C circuit,  V = 100 V and . Find the current in the circuit and the voltage across the capacitor and the resistor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox. 

Solution

Correct option is

0.25 A, 100 V, 7.5 V

The capacitor reactive of the circuit is  

            

                  

                .  

The impedance of the given R-C circuit is  

              

                

The (rms) current in the circuit is  

             

                    .  

The (rms) voltage across the capacitor is  

             

                  

                .  

and the across the resistor is 

             

                 

The sum of these is 100 V + 7.5 V = 107.5 V, which is greater than the source voltage (100 V). 

This is because the two voltages are not in phase, they are mutually perpendicular to each other.

SIMILAR QUESTIONS

Q1

A sinusoidal voltage V = 200 sin 314t is applied to a  resistor. Find the frequency of the supply.

Q2

In an a.c. circuit the peak voltage of supply is 300 V. What is rms voltage? What is mean voltage during a positive half-cycle and for a complete cycle?

Q3

 resistor is connected to 220 V-50 Hz a.c. supply. Find rms value of current in the circuit and the net power consumed for a complete cycle.

Q4

A 220 V-50 Hz a.c. supply is applied to a 44-mH inductor. What is rmscurrent in the circuit? What is the net power absorbed over a complete cycle?

Q5

A 110 V-60 Hz a.c. supply is applied to a  capacitor. What is rms current in the circuit? What is the net power absorbed over a complete cycle?

Q6

An alternating voltage E = 200 sin 300t is applied across a series combination of  and L = 800 mH. Calculate the impedance of the circuit.

Q7

A coil of inductance 0.50 H and resistance  is connected to a 240 V-50 Hz a.c. supply. What are the maximum current in the coil and the time lag between voltage maximum and current maximum?

Q8

An emf E = 100 sin 314t volt is applied across a pure capacitor of 637 . Find the instantaneous current i.

Q9

An a.c. voltage V = 200 sin 314t is applied across a series C-R circuit.Where . Find the capacitive reactance.

Q10

Calculate the rms current in an a.c. circuit containing a capacitor of  in series. The power supply in the circuit is rated 230 V, 50 Hz.