Download, print and study this document offline |
Page 1 CAPACITANCE 1. (i) q ? V ? q = CV q : Charge on positive plate of the capacitor C : Capacitance of capacitor. V : Potential difference between positive and negative plates. (ii) Representation of capacitor : , ( (iii) Energy stored in the capacitor : U = 2 1 CV 2 = C 2 Q 2 = 2 QV (iv) Energy density = 2 1 ? ? ? r E 2 = 2 1 ? ? ? K E 2 ? r = Relative permittivity of the medium. K= ? r : Dielectric Constant For vacuum, energy density = 2 1 ? ? E 2 (v) Types of Capacitors : (a) Parallel plate capacitor C = d A r 0 ? ? = K d A 0 ? A : Area of plates d : distance between the plates( << size of plate ) (b) Spherical Capacitor : ? Capacitance of an isolated spherical Conductor (hollow or solid ) C= 4 ? ? ? ? ? r R R = Radius of the spherical conductor ? Capacitance of spherical capacitor C= 4 ? ? ? ) a b ( ab ? 1 2 b a ? C = ) a b ( ab K 4 2 0 ? ? ? K 1 K 2 K 3 b a Page 2 CAPACITANCE 1. (i) q ? V ? q = CV q : Charge on positive plate of the capacitor C : Capacitance of capacitor. V : Potential difference between positive and negative plates. (ii) Representation of capacitor : , ( (iii) Energy stored in the capacitor : U = 2 1 CV 2 = C 2 Q 2 = 2 QV (iv) Energy density = 2 1 ? ? ? r E 2 = 2 1 ? ? ? K E 2 ? r = Relative permittivity of the medium. K= ? r : Dielectric Constant For vacuum, energy density = 2 1 ? ? E 2 (v) Types of Capacitors : (a) Parallel plate capacitor C = d A r 0 ? ? = K d A 0 ? A : Area of plates d : distance between the plates( << size of plate ) (b) Spherical Capacitor : ? Capacitance of an isolated spherical Conductor (hollow or solid ) C= 4 ? ? ? ? ? r R R = Radius of the spherical conductor ? Capacitance of spherical capacitor C= 4 ? ? ? ) a b ( ab ? 1 2 b a ? C = ) a b ( ab K 4 2 0 ? ? ? K 1 K 2 K 3 b a (c) Cylindrical Capacitor : ? >> {a,b} Capacitance per unit length = ) a / b ( n 2 ? ? ? ? ? F/m b ? (vi) Capacitance of capacitor depends on (a) Area of plates (b) Distance between the plates (c) Dielectric medium between the plates. (vii) Electric field intensity between the plates of capacitor E = 0 ? ? ? d V ? ? ? ?Surface change density (viii) Force experienced by any plate of capacitor : F = 0 2 A 2 q ? 2. DISTRIBUTION OF CHARGES ON CONNECTING TWO CHARGED CAPACITORS: When two capacitors are C 1 and C 2 are connected as shown in figure (a) Common potential : ? V = 2 1 2 2 1 1 C C V C V C ? ? = ce tan capaci Total e arg ch Total (b) Q 1 ' = C 1 V = 2 1 1 C C C ? (Q 1 + Q 2 ) Q 2 ' = C 2 V = 2 1 2 C C C ? (Q 1 +Q 2 ) Page 3 CAPACITANCE 1. (i) q ? V ? q = CV q : Charge on positive plate of the capacitor C : Capacitance of capacitor. V : Potential difference between positive and negative plates. (ii) Representation of capacitor : , ( (iii) Energy stored in the capacitor : U = 2 1 CV 2 = C 2 Q 2 = 2 QV (iv) Energy density = 2 1 ? ? ? r E 2 = 2 1 ? ? ? K E 2 ? r = Relative permittivity of the medium. K= ? r : Dielectric Constant For vacuum, energy density = 2 1 ? ? E 2 (v) Types of Capacitors : (a) Parallel plate capacitor C = d A r 0 ? ? = K d A 0 ? A : Area of plates d : distance between the plates( << size of plate ) (b) Spherical Capacitor : ? Capacitance of an isolated spherical Conductor (hollow or solid ) C= 4 ? ? ? ? ? r R R = Radius of the spherical conductor ? Capacitance of spherical capacitor C= 4 ? ? ? ) a b ( ab ? 1 2 b a ? C = ) a b ( ab K 4 2 0 ? ? ? K 1 K 2 K 3 b a (c) Cylindrical Capacitor : ? >> {a,b} Capacitance per unit length = ) a / b ( n 2 ? ? ? ? ? F/m b ? (vi) Capacitance of capacitor depends on (a) Area of plates (b) Distance between the plates (c) Dielectric medium between the plates. (vii) Electric field intensity between the plates of capacitor E = 0 ? ? ? d V ? ? ? ?Surface change density (viii) Force experienced by any plate of capacitor : F = 0 2 A 2 q ? 2. DISTRIBUTION OF CHARGES ON CONNECTING TWO CHARGED CAPACITORS: When two capacitors are C 1 and C 2 are connected as shown in figure (a) Common potential : ? V = 2 1 2 2 1 1 C C V C V C ? ? = ce tan capaci Total e arg ch Total (b) Q 1 ' = C 1 V = 2 1 1 C C C ? (Q 1 + Q 2 ) Q 2 ' = C 2 V = 2 1 2 C C C ? (Q 1 +Q 2 ) (c) Heat loss during redistribution : ?H = U i – U f = 2 1 2 1 2 1 C C C C ? (V 1 – V 2 ) 2 The loss of energy is in the form of Joule heating in the wire. 3. Combination of capacitor : (i) Series Combination 3 2 1 eq C 1 C 1 C 1 C 1 ? ? ? 3 2 1 3 2 1 C 1 : C 1 : C 1 V : V : V ? +Q V 1 V 2 V 3 C 2 C 1 C 3 –Q +Q –Q +Q –Q (ii) Parallel Combination : Q+ –Q C 3 C 2 C 1 V Q+ –Q Q+ –Q C eq = C 1 + C 2 + C 3 Q 1 : Q 2 :Q 3 = C 1 : C 2 : C 3 4. Charging and Discharging of a capacitor : (i) Charging of Capacitor ( Capacitor initially uncharged ): q = q 0 ( 1 – e – t / ? ) R V C q 0 = Charge on the capacitor at steady state q 0 = CV Page 4 CAPACITANCE 1. (i) q ? V ? q = CV q : Charge on positive plate of the capacitor C : Capacitance of capacitor. V : Potential difference between positive and negative plates. (ii) Representation of capacitor : , ( (iii) Energy stored in the capacitor : U = 2 1 CV 2 = C 2 Q 2 = 2 QV (iv) Energy density = 2 1 ? ? ? r E 2 = 2 1 ? ? ? K E 2 ? r = Relative permittivity of the medium. K= ? r : Dielectric Constant For vacuum, energy density = 2 1 ? ? E 2 (v) Types of Capacitors : (a) Parallel plate capacitor C = d A r 0 ? ? = K d A 0 ? A : Area of plates d : distance between the plates( << size of plate ) (b) Spherical Capacitor : ? Capacitance of an isolated spherical Conductor (hollow or solid ) C= 4 ? ? ? ? ? r R R = Radius of the spherical conductor ? Capacitance of spherical capacitor C= 4 ? ? ? ) a b ( ab ? 1 2 b a ? C = ) a b ( ab K 4 2 0 ? ? ? K 1 K 2 K 3 b a (c) Cylindrical Capacitor : ? >> {a,b} Capacitance per unit length = ) a / b ( n 2 ? ? ? ? ? F/m b ? (vi) Capacitance of capacitor depends on (a) Area of plates (b) Distance between the plates (c) Dielectric medium between the plates. (vii) Electric field intensity between the plates of capacitor E = 0 ? ? ? d V ? ? ? ?Surface change density (viii) Force experienced by any plate of capacitor : F = 0 2 A 2 q ? 2. DISTRIBUTION OF CHARGES ON CONNECTING TWO CHARGED CAPACITORS: When two capacitors are C 1 and C 2 are connected as shown in figure (a) Common potential : ? V = 2 1 2 2 1 1 C C V C V C ? ? = ce tan capaci Total e arg ch Total (b) Q 1 ' = C 1 V = 2 1 1 C C C ? (Q 1 + Q 2 ) Q 2 ' = C 2 V = 2 1 2 C C C ? (Q 1 +Q 2 ) (c) Heat loss during redistribution : ?H = U i – U f = 2 1 2 1 2 1 C C C C ? (V 1 – V 2 ) 2 The loss of energy is in the form of Joule heating in the wire. 3. Combination of capacitor : (i) Series Combination 3 2 1 eq C 1 C 1 C 1 C 1 ? ? ? 3 2 1 3 2 1 C 1 : C 1 : C 1 V : V : V ? +Q V 1 V 2 V 3 C 2 C 1 C 3 –Q +Q –Q +Q –Q (ii) Parallel Combination : Q+ –Q C 3 C 2 C 1 V Q+ –Q Q+ –Q C eq = C 1 + C 2 + C 3 Q 1 : Q 2 :Q 3 = C 1 : C 2 : C 3 4. Charging and Discharging of a capacitor : (i) Charging of Capacitor ( Capacitor initially uncharged ): q = q 0 ( 1 – e – t / ? ) R V C q 0 = Charge on the capacitor at steady state q 0 = CV ? ? ? ?Time constant = CR eq. I = ? 0 q e – t / ? ? ? ? ? R V e – t / ? (ii) Discharging of Capacitor : q = q 0 e – t / ? q 0 = Initial charge on the capacitor I = ? 0 q e – t / ? R C q 0 0.37v 0 ? t q 5. Capacitor with dielectric : (i) Capacitance in the presence of dielectric : C = d A K 0 ? = KC 0 + + + + + + + + + + + + + + ? ? ? 0 + + ? – – ? V ? b + – ? b – – – – – – – – – – – ? ? ? 0 b C 0 = Capacitance in the absence of dielectric. Page 5 CAPACITANCE 1. (i) q ? V ? q = CV q : Charge on positive plate of the capacitor C : Capacitance of capacitor. V : Potential difference between positive and negative plates. (ii) Representation of capacitor : , ( (iii) Energy stored in the capacitor : U = 2 1 CV 2 = C 2 Q 2 = 2 QV (iv) Energy density = 2 1 ? ? ? r E 2 = 2 1 ? ? ? K E 2 ? r = Relative permittivity of the medium. K= ? r : Dielectric Constant For vacuum, energy density = 2 1 ? ? E 2 (v) Types of Capacitors : (a) Parallel plate capacitor C = d A r 0 ? ? = K d A 0 ? A : Area of plates d : distance between the plates( << size of plate ) (b) Spherical Capacitor : ? Capacitance of an isolated spherical Conductor (hollow or solid ) C= 4 ? ? ? ? ? r R R = Radius of the spherical conductor ? Capacitance of spherical capacitor C= 4 ? ? ? ) a b ( ab ? 1 2 b a ? C = ) a b ( ab K 4 2 0 ? ? ? K 1 K 2 K 3 b a (c) Cylindrical Capacitor : ? >> {a,b} Capacitance per unit length = ) a / b ( n 2 ? ? ? ? ? F/m b ? (vi) Capacitance of capacitor depends on (a) Area of plates (b) Distance between the plates (c) Dielectric medium between the plates. (vii) Electric field intensity between the plates of capacitor E = 0 ? ? ? d V ? ? ? ?Surface change density (viii) Force experienced by any plate of capacitor : F = 0 2 A 2 q ? 2. DISTRIBUTION OF CHARGES ON CONNECTING TWO CHARGED CAPACITORS: When two capacitors are C 1 and C 2 are connected as shown in figure (a) Common potential : ? V = 2 1 2 2 1 1 C C V C V C ? ? = ce tan capaci Total e arg ch Total (b) Q 1 ' = C 1 V = 2 1 1 C C C ? (Q 1 + Q 2 ) Q 2 ' = C 2 V = 2 1 2 C C C ? (Q 1 +Q 2 ) (c) Heat loss during redistribution : ?H = U i – U f = 2 1 2 1 2 1 C C C C ? (V 1 – V 2 ) 2 The loss of energy is in the form of Joule heating in the wire. 3. Combination of capacitor : (i) Series Combination 3 2 1 eq C 1 C 1 C 1 C 1 ? ? ? 3 2 1 3 2 1 C 1 : C 1 : C 1 V : V : V ? +Q V 1 V 2 V 3 C 2 C 1 C 3 –Q +Q –Q +Q –Q (ii) Parallel Combination : Q+ –Q C 3 C 2 C 1 V Q+ –Q Q+ –Q C eq = C 1 + C 2 + C 3 Q 1 : Q 2 :Q 3 = C 1 : C 2 : C 3 4. Charging and Discharging of a capacitor : (i) Charging of Capacitor ( Capacitor initially uncharged ): q = q 0 ( 1 – e – t / ? ) R V C q 0 = Charge on the capacitor at steady state q 0 = CV ? ? ? ?Time constant = CR eq. I = ? 0 q e – t / ? ? ? ? ? R V e – t / ? (ii) Discharging of Capacitor : q = q 0 e – t / ? q 0 = Initial charge on the capacitor I = ? 0 q e – t / ? R C q 0 0.37v 0 ? t q 5. Capacitor with dielectric : (i) Capacitance in the presence of dielectric : C = d A K 0 ? = KC 0 + + + + + + + + + + + + + + ? ? ? 0 + + ? – – ? V ? b + – ? b – – – – – – – – – – – ? ? ? 0 b C 0 = Capacitance in the absence of dielectric. (ii) E in = E – E ind = 0 ? ? – 0 b ? ? = 0 K ? ? = d V E : 0 ? ? Electric field in the absence of dielectric E ind : Induced (bound) charge density. (iii) ? b = ?(1 – K 1 ). 6. Force on dielectric (i) When battery is connected d 2 V ) 1 K ( b F 2 0 ? ? ? + – b b ? ? d ? ? ? F x (ii) When battery is not connected F = 2 2 C 2 Q dx dC * Force on the dielectric will be zero when the dielectric is fully inside.Read More
97 videos|336 docs|104 tests
|
|
Explore Courses for NEET exam
|