NCERT Solutions Class 12th Physics Chapter – 7 Alternating Current
| Textbook | NCERT |
| class | Class – 12th |
| Subject | Physics |
| Chapter | Chapter – 7 |
| Chapter Name | Alternating Current |
| Category | Class 12th Physics Notes in English |
| Medium | English |
| Source | Last Doubt |
NCERT Solutions Class 12th Physics Chapter – 7 Alternating Current
?Chapter – 7?
✍Alternating Current✍
?Notes?
In a pure ohmic resistance both alternating current and e.m.f. are in the same phase.
Alternating e.m.f. leads the alternating current by π2 in a pure inductance.
In a pure capacitor circuit, the alternating e.m.f. lags behind the alternating current by π2.
xL = ωL is called inductive reactance.
xC = 1ωC is called capacitance reactance.
Resistance, reactance, and impedance all are measured in ohm.
The graph between xL and ω is a straight line.
The applied voltage is equal to the potential drop across the resistance R at the resonant frequency in the LCR circuit.
Power is dissipated only due to the ohmic resistance in an a.c. circuit.
Thus in an RC or RL a.c. the circuit power is dissipated only due to R and not due to its inductance or capacitance.
Resonant angular frequency is the same both for the series and parallel resonant circuit.
The graph between xC and w is a hyperbola.
The maximum value of current is I = ErmsRat the resonant angular frequency W = W0.
As ω to increases, Z of parallel LCR resonant circuit first increases becomes maximum and then decreases.
For series LCR resonant circuit, Z first decreases become minimum and then increases.
The power rating of an element used in a.c. circuit refers to its average power rating.
The power consumed in an a.c. the circuit is never negative.
→For very high frequency of a.c., the inductor behaves as an open circuit and the capacitor behaves as a conductor.
The impedance of the LR circuit depends upon the frequency of a.c. The phase angle between E and I in an LR circuit also depends upon the frequency.
As the frequency of a.e. increases, the impedance of the CR circuit decreases.
Electrical resonance takes place when the amplitude of the current in the circuit is maximum and impedance is minimum and the LCR circuit is a purely resistive circuit.
For purely resistive circuit, power factor = 1.
For purely inductive and capacitive circuits, the power factor is zero. Choke coil is used to control a.c. without much loss of electric power.
K > 1 for step-up transformer and K < 1 for step down transformer. Transformer works on the principle of mutual inductance. q = 100% and Eplp = EsIs for an ideal transformer.
The power consumed in a circuit is never negative.
A.C. – It is defined as the? electric current magnitude of which changes with time and reverses its direction periodically.
Average or Mean Value of A.C. – It is defined as that steady current which when passed through a circuit for a half time period of A.C. produces the same amount of charge as is being produced by A.C. in the same time and in the same circuit.
R.M.S. value or effective value of A.C. – It is defined as that steady current that produces the same amount of heat in resistance in a given time as is being done by a.c. passed through the same circuit for the same time.
Inductive reactance – It is the effective opposition offered by the inductor to the flow of a.c. in the circuit.
Capacitive reactance – It is the effective opposition offered by the capacitor to the flow of a.c. in the circuit.
Q-factor of series LCR circuit – It is defined as the ratio of the voltage drop across inductor (or capacitor) to the applied voltage.
Power of an a.c. circuit – It is the product of instantaneous e.m.f. and instantaneous current in the circuit.
Power factor – It is defined as the ratio of average power to the apparent power.
Idle or wattless current – It is the current due to the flow of which no power is consumed in an a.c. circuit.
° Transformer’s a device used to convert low alternating voltage at high current into a high voltage at low current or vice-versa.
Important Formulae
Erms = 12√ E0 = E virtual = Eeff
Irms = 12√ I0
Instantaneous e.m.f. is given by E = E0 sin ωt
In a purely inductive circuit, current lags behind E by π2
I = I0 sin (ωt – π2)
In a purely capacitive circuit
I = I0 sin (ωt + π2)
XL = ωL = 2πvL = E0I0=EvFv
XL = 1ωC=12πvC=E0I0=EvIv
Average value of induced a.c. over a complete cycle is –
Average power = apparent power × power factor
or
Pav = Ev Iv cos Φ.
cos Φ = RZ
Resonant angular frequency of LCR series circuit is given by
ω0 = 1LC√
or
v0 = 12πLC√
Impedence of LCR series circuit is given by
Z = R2+(XL−XC)2−−−−−−−−−−−−−−√
= R2+(ωL−1ωC)2−−−−−−−−−−−−−−√
Tangent of the phase angle is given by .
tan Φ = XL−XCR
Power factor of LR circuit is given by
cos Φ = RZ=RR2+X2L√
tan Φ = xLR=ωLR
For CR. circuit,
tan Φ = XCR=1RωC
Z = R2+X2c−−−−−−−√=R2+(1ωC)2−−−−−−−−−√
For a transformer,
K = NsNp=ϕsϕ˙p=EsEp=IpIs
For an ideal transformer,
When Zp and Zs are called impedance of primary and secondary coil of the transformer.
Efficiency of a transformer is given by,
η = output power input power
= EsIsEpIp.
Maximum e.m.f. induced in a coil is given by e0 = NBAω.
where N = No. of turns of the coil.
A = Area of the coil.
ω = angular frequency of rotation of the coil.
B = magnetic field.
Q.factor = XLIRI=ω0 LR=1ω0CR=1RLC−−√