Question

19. In an AC circuit with all components connected in
series, the emf and the current are given by
TC
V=200 sin 314t +
volt and I=5 sin 314t ampere.
6
중
27.
Obtain (1) the peak values of emf and current, (i) the
frequency of the AC source, (iii) the phase difference
between V and I (iv) impedance of the circuit

Answer 1

Answer:

19. In an AC circuit with all components connected in

series, the emf and the current are given by

TC

V=200 sin 314t +

volt and I=5 sin 314t ampere.

6

중

27.

Obtain (1) the peak values of emf and current, (i) the

frequency of the AC source, (iii) the phase difference

between V and I (iv) impedance of the circuit

Explanation:

don't no

Answer 2

Given:

$V=200sin(314t)V$

$I=5 sin(314t)A$

To find:

1. Peak value of EMF and current.
2. Frequency of the AC source.
3. Phase difference between V and I.
4. Impedance of the circuit.

Solution:

Step 1

Standard form of equation is $A=A_{o}sin$ω$t$ ; where $A_{o}$ is the peak value.

We have been given the equations for a variable EMF and current with respect to time t.

Hence,

Peak value of EMF = $200V$

Peak value of Current = $5A$

Step 2

If we consider the standard form of an equation for current,

$I=I_{o}sin$(ω$t$)

Comparing it with the given equation,

We get  ω$t$ $=314t$

We know,  ω = 2πf ; where f is the frequency

Hence,

$2$πf $=314$

$2(3.14)f=314$

$f=50Hz$

Hence, frequency is $50Hz.$

Step 3

We know, if in a circuit, only resistor is present, then the current and voltage in the circuit work in the same phase.

Hence, Phase difference between V and I is 0.

Step 4

We know,

Impedance in a circuit is given by $Z$ , here, in the circuit, Inductor and capacitor is not present hence, the impedance in the circuit will be solely the resistance in the circuit.

$Z=R$

Using Ohm's law, $I=\frac{V}{Z}$

Hence, $Z=\frac{V}{I}$    or  $R=\frac{V}{I}$

Substituting the given values, we get

$R=\frac{200}{5}$  $;$ $or$

$R=40$Ω

Hence, the impedance of the circuit is 40Ω.

Final answer:

Hence,

1. Peak value of current is 5A and peak value of EMF is 200V.
2. Frequency of the AC source is 50 Hz.
3. Phase difference between V and I is $0^{o}$.
4. Impedance of the circuit is 40Ω.