{"id":34984,"date":"2022-11-21T17:14:58","date_gmt":"2022-11-21T11:44:58","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=34984"},"modified":"2022-11-23T16:18:41","modified_gmt":"2022-11-23T10:48:41","slug":"ts-inter-2nd-year-physics-notes-chapter-10","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-10\/","title":{"rendered":"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current"},"content":{"rendered":"<p>Here students can locate <a href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes\/\">TS Inter 2nd Year Physics Notes<\/a> 10th Lesson Alternating Current to prepare for their exam.<\/p>\n<h2>TS Inter 2nd Year Physics Notes 10th Lesson Alternating Current<\/h2>\n<p>\u2192 Alternating Current (AC): If the supplied voltage varies like a sine function then it is called &#8220;alternating voltage&#8221; and the current driven in the circuit is called &#8220;alternating current&#8221;.<\/p>\n<p>\u2192 Preference of AC:<\/p>\n<ul>\n<li>We prefer AC supply to DC supply because it is easy to produce.<\/li>\n<li>It can be easily transformed from high voltage to low voltage or from low voltage to high voltage. 3) It is easy to transmit to longer distances with less line losses.<\/li>\n<\/ul>\n<p>\u2192 AC Voltage applied to a Resistor: When a AC Voltage V = V<sub>m<\/sub> sin cot is applied to a pure resistor then current, I = \\(\\frac{V_m}{R}\\) sin \u03c9t = \\(\\frac{\\mathrm{V}}{\\mathrm{R}}\\) and I<sub>m<\/sub> = \\(\\frac{V_m}{R}\\)<br \/>\nIn a pure resistor applied voltage and current through resistor are in phase, i.e., when voltage is maximum then current is also maximum. Similarly when voltage is minimum the current is also minimum.<\/p>\n<p>\u2192 Average power consumed in a resistor P = \\(\\frac{1}{2}\\)I<sub>m<\/sub><sup>2<\/sup> R(or) P = I<sup>2<\/sup>R = VI (\u2235I = I<sub>m<\/sub>\/\u221a2)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 AC Voltage through an Inductor: in a pure inductor (i.e., where resistance R = 0) applied voltage V = V<sub>m<\/sub> sin \u03c9<sub>0<\/sub>t.<br \/>\nCurrent through inductor I = I<sub>m<\/sub> sin (\u03c9t &#8211; \u03c0\/2) In a pure inductor current lags behind<br \/>\nvoltage by a phase angle \u03a6 = \\(\\frac{\\pi}{2}\\)<br \/>\nReactance of Inductor X<sub>L<\/sub> = \u03c9<sub>L<\/sub><br \/>\nI<sub>m<\/sub> = \\(\\frac{V_m}{X_L}\\)<\/p>\n<p>\u2192 AC Voltage through a pure Capacitor:<br \/>\nWhen AC voltage is applied to a pure capacitor its reactance X<sub>c<\/sub> = \\(\\frac{1}{\\omega \\mathrm{C}}\\). (called capacitive reactance)<br \/>\nVoltage across capacitor V = V<sub>m<\/sub> sin \u03c9t<br \/>\nCurrent in the capacitor I = I<sub>m<\/sub> sin (\u03c9t + \\(\\frac{\\pi}{2}\\)) In a capacitor current (I) leads the applied voltage by an angle \\(\\frac{\\pi}{2}\\).<br \/>\nPower dissipation in a pure capacitor P<sub>c<\/sub> = 0<\/p>\n<p>\u2192 Reactance: The resistance of active components like Inductance (L) and Capacitance (C) changes with frequency (co) of current supplied.<br \/>\nThe resistance that changes with frequency is called reactance (X).<br \/>\nReactance of Inductance = X<sub>L<\/sub> = \u03c9L<br \/>\nReactance of capacitance = X<sub>C<\/sub> = \\(\\frac{1}{\\omega \\mathrm{C}}\\)<\/p>\n<p>\u2192 Impedance (Z): The total resistance of a circuit with reactive components like inductance or capacitance or both along with resistance &#8216;R&#8217; is given by Z = R + X<sub>C<\/sub> + X<sub>L<\/sub><br \/>\nThe total resistance of a circuit with reactive components is called Impedance.<br \/>\nImpedence (Z) of R-L circuit Z = R + \u03c9L<br \/>\nImpedance of C &#8211; R circuit Z = \\(\\sqrt{R^2+\\left(\\frac{1}{\\omega C}\\right)^2}\\)<br \/>\nImpedance of L &#8211; C circuit Z = \\(\\sqrt{\\left(\\omega L-\\frac{1}{\\omega \\mathrm{C}}\\right)^2}\\)<\/p>\n<p>\u2192 Phasor diagram: Phasor diagram represents the current in a circuit which contains resistance (R) and reactive components like inductance (L) and capacitance &#8216;C&#8217;.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34988\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-2nd-Year-Physics-Notes-Chapter-10-Alternating-Current-1.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current 1\" width=\"154\" height=\"194\" \/><\/p>\n<p>\u2192 In a circuit let I is the phasor represents the current it is always parallel to VR i.e., vol\u00actage along resistance.<br \/>\nVoltage across capacitor V<sub>c<\/sub> lags behind I by an angle \\(\\frac{\\pi}{2}\\).<br \/>\nVoltage across inductor VR leads current phasor I by an angle \\(\\frac{\\pi}{2}\\)<br \/>\nPhasor relation is V = V<sub>R<\/sub> + V<sub>L<\/sub> + V<sub>c<\/sub><\/p>\n<p>\u2192 Impedance diagram: Graphical represen-tation impedance of Z = \\(\\sqrt{\\mathrm{R}^2+\\left(\\mathrm{X}_{\\mathrm{C}}-\\mathrm{X}_{\\mathrm{L}}\\right)^2}\\) in the form of a right angle triangle is called &#8220;impedance diagram&#8221;.<\/p>\n<p>\u2192 Impedance diagram<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34987\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-2nd-Year-Physics-Notes-Chapter-10-Alternating-Current-2.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current 2\" width=\"175\" height=\"196\" \/><br \/>\nWhere<br \/>\nX &#8211; direction represents Resistance R.<br \/>\nY &#8211; direction represents total reactance (X<sub>C<\/sub> &#8211; X<sub>L<\/sub>) and Hypotenuse represents impedance.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Series LCR Circuit: In series LCR circuit an inductance (L), capacitance &#8216;C&#8217; and resistance &#8216;R&#8217; are connected to an AC source. AC voltage through LCR ciruit. Let a voltage V = V<sub>m<\/sub> sin cot is applied to series LCR circuit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34986\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/11\/TS-Inter-2nd-Year-Physics-Notes-Chapter-10-Alternating-Current-3.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current 3\" width=\"240\" height=\"163\" \/><br \/>\nTotal voltage in the circuit V = V<sub>L<\/sub> + V<sub>R<\/sub> + V<sub>C<\/sub><br \/>\nImpedance of circuit,<br \/>\nZ = \\(\\sqrt{R^2+\\left(X_C-X_L\\right)^2}=\\sqrt{R^2+\\left(\\omega L-\\frac{1}{\\omega C}\\right)^2}\\)<br \/>\nMaximum current I<sub>m<\/sub> = \\(\\frac{\\mathrm{V}_{\\mathrm{m}}}{\\mathrm{Z}}\\)<br \/>\nPhase angle \u03a6 = tan\\(\\left(\\frac{\\mathrm{X}_{\\mathrm{C}}-\\mathrm{X}_{\\mathrm{L}}}{\\mathrm{R}}\\right)\\)<br \/>\nResonating frequency, \u03c9<sub>0<\/sub> = \\(\\frac{1}{\\sqrt{\\mathrm{LC}}}\\)<\/p>\n<p>\u2192 Resonance: Resonance is a physical phenomenon at which a system tends to oscillate freely. This particular frequency is called natural frequency. At resonance amplitude of oscillations is large.<\/p>\n<p>\u2192 Series LCR circuit-Resonant frequency:<br \/>\nResonant frequency of series LCR circuit is \u03c9<sub>0<\/sub> = \\(\\frac{1}{\\sqrt{\\mathrm{LC}}}\\)<\/p>\n<p>\u2192 Sharpness of resonance: In case of series LCR circuit resonant frequency \u03c9<sub>0<\/sub> = \\(\\frac{1}{\\sqrt{\\mathrm{LC}}}\\)<br \/>\nHowever the amplitude of oscillation is high in between the frequencies \u03c9<sub>2<\/sub> = \u03c9<sub>0<\/sub> + \u0394\u03c9 and \u03c9<sub>1<\/sub> = \u03c9<sub>0<\/sub> &#8211; \u0394\u03c9. Where \u0394\u03c9 is a small frequency change from \u03c9<sub>0<\/sub>?<br \/>\n\u03c9<sub>2<\/sub> &#8211; \u03c9<sub>1<\/sub> = 2\u0394\u03c9 is called band width of resonance, \u03c9<sub>0<\/sub>\/2\u0394\u03c9 is called sharpness of resonance.<br \/>\nNote: Tuning circuits with sharp resonance are considered as very good frequency selectors.<\/p>\n<p>\u2192 Power of AC circuit and Power factor:<br \/>\nPower of AC circuit P = I<sup>2<\/sup>Z cos\u03a6. It indicates that power depends not only on current I and Impedance Z of circuit but also cosine of phase angle between I and Z.<br \/>\nThe term cos \u03a6 is called power factor.<\/p>\n<p>\u2192 Wattless current: In a circuit with pure inductance or pure capacitance the phase angle between voltage and currents are \u03a6 = \\(\\frac{\\pi}{2}\\), so cos \u03a6 = 0. hence no power is dissipated through then even though current passes through them. This current is referred as wattless current.<\/p>\n<p>\u2192 Transformer: A transformer works on the principle of electromagnetic induction&#8221;. A transformer will convert high voltage AC current into low voltage AC current or Low voltage AC current into high voltage AC current by keeping VI = constant.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 Turns ratio: The ratio of number of turns in primary coil (N<sub>p<\/sub>) to number of turns in secondary coil (N<sub>s<\/sub>) is called &#8220;transformer turns ratio&#8221;.<br \/>\nVoltage at secondary, V<sub>s<\/sub> = \\(\\)V<sub>p<\/sub> and<br \/>\nCurrent at secondary, I<sub>s<\/sub> = \\(\\)I<sub>p<\/sub><\/p>\n<p>Note:<\/p>\n<ul>\n<li>Transformers with N<sub>s<\/sub>\/ N<sub>p<\/sub> &gt; 1 are called step up transformers.<\/li>\n<li>Transformers with N<sub>s<\/sub> \/ N<sub>p<\/sub> &lt; 1 are called step down transformers.<\/li>\n<li>A transformer will work for a.c currents only.<\/li>\n<li>The Equation V<sub>s<\/sub> = \\(\\left(\\frac{\\mathrm{N}_{\\mathrm{s}}}{\\mathrm{N}_{\\mathrm{p}}}\\right)\\)V<sub>p<\/sub> is applicable for ideal transformers. But in real case a small amount of energy (less than 5%) is wasted due to\n<ul>\n<li>Flux leakage<\/li>\n<li>Resistance of windings<\/li>\n<li>Eddy currents and<\/li>\n<li>Hysteresis.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u2192 In AC circuits: Voltage at any instant V = V<sub>m<\/sub> sin cot current at any instant I = I<sub>m<\/sub> sin cot (where I<sub>m<\/sub> = \\(\\frac{V_m}{R}\\))<\/p>\n<p>\u2192 Root mean square values (R.M.S Values):<br \/>\nR.M.S. value of current I = I<sub>m<\/sub> \/ \u221a2 = 0.707 I<sub>m<\/sub><br \/>\nR.M.S. value of voltage V = V<sub>m<\/sub> \/\u221a2 = 0.707 V<sub>m<\/sub><br \/>\nAverage power<br \/>\nP\u0305 = \\(\\frac{1}{2}\\)I<sub>m<\/sub><sup>2<\/sup>R = \\(\\frac{1}{2}\\)Iv<sup>2<\/sup>\/R = \\(\\frac{1}{2}\\)I<sub>m<\/sub>V<sub>m<\/sub><\/p>\n<p>\u2192 Relation between V and I: V<sub>m<\/sub> = I<sub>m<\/sub> R and V<br \/>\n= I R and P = VI = I<sup>2<\/sup>R = \\(\\frac{\\mathrm{V}^2}{\\mathrm{R}}\\).<\/p>\n<p>\u2192 In pure Inductors : V = V<sub>m<\/sub> sin \u03c9t ; I = I<sub>m<\/sub> (sin \u03c9t &#8211; \u03c0\/2)<br \/>\nIn inductance current lags behind voltage by 90\u00b0 or \\(\\frac{\\pi}{2}\\) radians.<br \/>\nInductive reactance X<sub>L<\/sub> = \u03c9L = 2\u03c0\u03c5L<br \/>\nMaximum current through inductor I<sub>m<\/sub> = \\(\\frac{\\mathrm{V}_{\\mathrm{m}}}{\\mathrm{X}_{\\mathrm{L}}}\\)<\/p>\n<p>\u2192 In pure Capacitors : Voltage across capacitor V = \\(\\frac{q}{c}\\) = V<sub>m<\/sub> sin \u03c9t.<br \/>\nCurrent in capacitor I = I<sub>m<\/sub> sin (\u03c9t + \u03c0\/2).<br \/>\nIn a pure capacitor current I leads voltage V by a phase angle 90\u00b0 or \\(\\frac{\\pi}{2}\\) radians.<br \/>\nReactance of capacitor X<sub>c<\/sub> = \\(\\frac{1}{\\omega \\mathrm{C}}\\); Maximum current I<sub>m<\/sub> = \\(\\frac{V_m}{(1 \/ \\omega c)}=\\frac{V_m}{X_c}\\)<br \/>\nInstantaneous power supplied P<sub>c<\/sub> = \\(\\frac{\\mathrm{i}_{\\mathrm{m}} \\cdot \\mathrm{V}_{\\mathrm{m}}}{2}\\) sin 2\u03c9t.<br \/>\nPower supplied to capacitor over one complete cycle is zero.<\/p>\n<p>\u2192 In a resistor: Applied Voltage V = V<sub>m<\/sub> sin \u03c9t<br \/>\nCurrent I = \\(\\frac{I_m}{R}=\\frac{V_m}{R}\\) sin \u03c9t<br \/>\nAverage power dissipated<br \/>\nP\u0305 = \\(\\frac{1}{2}\\)I2mR = \\(\\frac{V^2}{R}\\) = VI = \\(\\frac{\\mathrm{V}_{\\mathrm{m}} \\mathrm{I}_{\\mathrm{m}}}{2}\\).<\/p>\n<p>\u2192 In series LCR circuit,<br \/>\nTotal potential in circuit V = V<sub>L<\/sub> + V<sub>R<\/sub> + V<sub>c<\/sub>.<br \/>\n= V<sub>m<\/sub>\/\\(\\frac{V_m}{Z}\\)<br \/>\nImpedance of circuit Z = \\(\\sqrt{\\mathrm{R}^2+\\left(\\mathrm{X}_{\\mathrm{C}}-\\mathrm{X}_{\\mathrm{L}}\\right)^2}\\)<br \/>\nPhase difference \u03a6 = tan<sup>-1<\/sup>\\(\\left[\\frac{\\mathrm{X}_{\\mathrm{C}}-\\mathrm{X}_{\\mathrm{L}}}{\\mathrm{R}}\\right]\\)<\/p>\n<p>Resonant frequency \u03c9<sub>0<\/sub> = \\(\\frac{1}{\\sqrt{\\mathrm{LC}}}\\)<br \/>\nAt Resonance \u03c9L = \\(\\frac{1}{\\omega \\mathrm{C}}\\) and Impedance Z = R.<br \/>\nBand width of circuit 2\u0394\u03c9 = \u03c9<sub>2<\/sub> &#8211; \u03c9<sub>1<\/sub><br \/>\n(where \u03c9<sub>2<\/sub> &gt; \u03c9<sub>1<\/sub>)<br \/>\nSharpness of circuit Q = \\(\\frac{\\omega_0}{2 \\Delta \\omega}=\\frac{\\omega_0 L}{R}\\)<br \/>\nPower in AC circuit P = I<sup>2<\/sup>Zcos \u03a6 = VIcos \u03a6<br \/>\nwhere is phase between voltage V and current I.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/tsboardsolutions.com\/wp-content\/uploads\/2022\/10\/TS-Board-Solutions.png\" alt=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\" width=\"183\" height=\"15\" \/><\/p>\n<p>\u2192 In LC CircuIt : Electrical energy stored In charged capacitor U<sub>E<\/sub> = \\(\\) where q<sub>m<\/sub> = I<sub>m<\/sub>\/\u03c9<sub>0<\/sub><br \/>\nResonant frequency \u03c9<sub>0<\/sub> = \\(\\frac{1}{\\sqrt{\\mathrm{LC}}}\\)<br \/>\nIn transformer;<br \/>\nTurns ratio = \\(\\frac{\\mathrm{N}_{\\mathrm{s}}}{\\mathrm{N}_{\\mathrm{p}}}\\)<br \/>\nSecondary voltage V<sub>s<\/sub> = \\(\\left[\\frac{\\mathrm{N}_{\\mathrm{s}}}{\\mathrm{N}_{\\mathrm{p}}}\\right]\\)V<sub>p<\/sub><br \/>\nSecondary current I<sub>s<\/sub> = \\(\\left[\\frac{\\mathrm{N}_{\\mathrm{p}}}{\\mathrm{N}_{\\mathrm{s}}}\\right]\\)I<sub>p<\/sub><br \/>\nBack emf in primary V<sub>p<\/sub> = -N<sub>p<\/sub> \\(\\frac{\\mathrm{d} \\phi}{\\mathrm{dt}}\\)<br \/>\nInduced emf or voltage in secondary V<sub>s<\/sub> = N<sub>s<\/sub> \\(\\frac{\\mathrm{d} \\phi}{\\mathrm{dt}}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here students can locate TS Inter 2nd Year Physics Notes 10th Lesson Alternating Current to prepare for their exam. TS Inter 2nd Year Physics Notes 10th Lesson Alternating Current \u2192 Alternating Current (AC): If the supplied voltage varies like a sine function then it is called &#8220;alternating voltage&#8221; and the current driven in the circuit &#8230; <a title=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\" class=\"read-more\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-10\/\" aria-label=\"More on TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[26],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current - TS Board Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-physics-notes-chapter-10\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"TS Inter 2nd Year Physics Notes Chapter 10 Alternating Current - TS Board Solutions\" \/>\n<meta property=\"og:description\" content=\"Here students can locate TS Inter 2nd Year Physics Notes 10th Lesson Alternating Current to prepare for their exam. 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TS Inter 2nd Year Physics Notes 10th Lesson Alternating Current \u2192 Alternating Current (AC): If the supplied voltage varies like a sine function then it is called &#8220;alternating voltage&#8221; and the current driven in the circuit ... 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