Page 1 Module 2 : Electrostatics Lecture 11 : Capacitance Objectives In this lecture you will learn the following Capacitors in series and in parallel Properties of dielectric Conductor and dielectric in an electric field. Polarization and bound charges Gauss's Law for dielectrics Capacitors in Combination : Capacitors can be combined in series or parallel combinations in a circuit. Parallel Combination When they are in parallel, the potential difference across each capacitor is the same. The charge on each capacitor is obtained by multiplying with the capacitance, i.e. . Page 2 Module 2 : Electrostatics Lecture 11 : Capacitance Objectives In this lecture you will learn the following Capacitors in series and in parallel Properties of dielectric Conductor and dielectric in an electric field. Polarization and bound charges Gauss's Law for dielectrics Capacitors in Combination : Capacitors can be combined in series or parallel combinations in a circuit. Parallel Combination When they are in parallel, the potential difference across each capacitor is the same. The charge on each capacitor is obtained by multiplying with the capacitance, i.e. . Since total charge in the capacitors is sum of all the charges, the effective capacitance of the combination is Series Combination : When capacitors are joined end to end in series, the first capacitor gets charged and induces an equal charge on the second capacitor which is connected to it. This in turn induces an equal charge on the third capacitor, and so on. The net potential difference between the positive plate of the first capacitor and the negative plate of the last capacitor in series is The individual voltage drops are so that The effective capacitance is, therefore, given by Example 19 Calculate the voltage across the 5 F capacitor in the following circuit. Page 3 Module 2 : Electrostatics Lecture 11 : Capacitance Objectives In this lecture you will learn the following Capacitors in series and in parallel Properties of dielectric Conductor and dielectric in an electric field. Polarization and bound charges Gauss's Law for dielectrics Capacitors in Combination : Capacitors can be combined in series or parallel combinations in a circuit. Parallel Combination When they are in parallel, the potential difference across each capacitor is the same. The charge on each capacitor is obtained by multiplying with the capacitance, i.e. . Since total charge in the capacitors is sum of all the charges, the effective capacitance of the combination is Series Combination : When capacitors are joined end to end in series, the first capacitor gets charged and induces an equal charge on the second capacitor which is connected to it. This in turn induces an equal charge on the third capacitor, and so on. The net potential difference between the positive plate of the first capacitor and the negative plate of the last capacitor in series is The individual voltage drops are so that The effective capacitance is, therefore, given by Example 19 Calculate the voltage across the 5 F capacitor in the following circuit. Solution : The equivalent circuit is shown above.The two 10 capacitors in series is equivalent to a 5 capacitor.5 in parallel with this equivalent capacitor gives 10 as the next equivalent.The circuit therefore consists of a 10 in series with the 20 capacitor. Since charge remains constant in a series combination, the potential drop across the 10 capacitor is twice as much as that across 20 capacitor. The voltage drop across the 10 (and hence across the given 5 ) is V. Exercise 2 Determine the effective capacitance of the following capacitance circuit and find the voltage across each capacitance if the voltage across the points a and b is 300 V. Page 4 Module 2 : Electrostatics Lecture 11 : Capacitance Objectives In this lecture you will learn the following Capacitors in series and in parallel Properties of dielectric Conductor and dielectric in an electric field. Polarization and bound charges Gauss's Law for dielectrics Capacitors in Combination : Capacitors can be combined in series or parallel combinations in a circuit. Parallel Combination When they are in parallel, the potential difference across each capacitor is the same. The charge on each capacitor is obtained by multiplying with the capacitance, i.e. . Since total charge in the capacitors is sum of all the charges, the effective capacitance of the combination is Series Combination : When capacitors are joined end to end in series, the first capacitor gets charged and induces an equal charge on the second capacitor which is connected to it. This in turn induces an equal charge on the third capacitor, and so on. The net potential difference between the positive plate of the first capacitor and the negative plate of the last capacitor in series is The individual voltage drops are so that The effective capacitance is, therefore, given by Example 19 Calculate the voltage across the 5 F capacitor in the following circuit. Solution : The equivalent circuit is shown above.The two 10 capacitors in series is equivalent to a 5 capacitor.5 in parallel with this equivalent capacitor gives 10 as the next equivalent.The circuit therefore consists of a 10 in series with the 20 capacitor. Since charge remains constant in a series combination, the potential drop across the 10 capacitor is twice as much as that across 20 capacitor. The voltage drop across the 10 (and hence across the given 5 ) is V. Exercise 2 Determine the effective capacitance of the following capacitance circuit and find the voltage across each capacitance if the voltage across the points a and b is 300 V. [Ans. 8 F., 100V,200V,200V,200V,200V,100V] Conductors and Dielectric A conductor is characterized by existence of free electrons . These are electrons in the outermost shells of atoms (the valence electrons) which get detatched from the parent atoms during the formation of metallic bonds and move freely in the entire medium in such way that the conductor becomes an equipotential volume. In contrast, in dielectrics (insulators), the outer electrons remain bound to the atoms or molecules to which they belong. Both conductors and dielectric, on the whole, are charge neutral. However, in case of dielectrics, the charge neutrality is satisfied over much smaller regions (e.g. at molecular level). Polar and non-polar molecules : A dielectric consists of molecules which remain locally charge neutral. The molecules may be polar or non-polar. In non-polar molecules, the charge centres of positive and negative charges coincide so that the net dipole moment of each molecule is zero. Carbon dioxide molecule is an example of a non-polar molecule. Click here for Animation Page 5 Module 2 : Electrostatics Lecture 11 : Capacitance Objectives In this lecture you will learn the following Capacitors in series and in parallel Properties of dielectric Conductor and dielectric in an electric field. Polarization and bound charges Gauss's Law for dielectrics Capacitors in Combination : Capacitors can be combined in series or parallel combinations in a circuit. Parallel Combination When they are in parallel, the potential difference across each capacitor is the same. The charge on each capacitor is obtained by multiplying with the capacitance, i.e. . Since total charge in the capacitors is sum of all the charges, the effective capacitance of the combination is Series Combination : When capacitors are joined end to end in series, the first capacitor gets charged and induces an equal charge on the second capacitor which is connected to it. This in turn induces an equal charge on the third capacitor, and so on. The net potential difference between the positive plate of the first capacitor and the negative plate of the last capacitor in series is The individual voltage drops are so that The effective capacitance is, therefore, given by Example 19 Calculate the voltage across the 5 F capacitor in the following circuit. Solution : The equivalent circuit is shown above.The two 10 capacitors in series is equivalent to a 5 capacitor.5 in parallel with this equivalent capacitor gives 10 as the next equivalent.The circuit therefore consists of a 10 in series with the 20 capacitor. Since charge remains constant in a series combination, the potential drop across the 10 capacitor is twice as much as that across 20 capacitor. The voltage drop across the 10 (and hence across the given 5 ) is V. Exercise 2 Determine the effective capacitance of the following capacitance circuit and find the voltage across each capacitance if the voltage across the points a and b is 300 V. [Ans. 8 F., 100V,200V,200V,200V,200V,100V] Conductors and Dielectric A conductor is characterized by existence of free electrons . These are electrons in the outermost shells of atoms (the valence electrons) which get detatched from the parent atoms during the formation of metallic bonds and move freely in the entire medium in such way that the conductor becomes an equipotential volume. In contrast, in dielectrics (insulators), the outer electrons remain bound to the atoms or molecules to which they belong. Both conductors and dielectric, on the whole, are charge neutral. However, in case of dielectrics, the charge neutrality is satisfied over much smaller regions (e.g. at molecular level). Polar and non-polar molecules : A dielectric consists of molecules which remain locally charge neutral. The molecules may be polar or non-polar. In non-polar molecules, the charge centres of positive and negative charges coincide so that the net dipole moment of each molecule is zero. Carbon dioxide molecule is an example of a non-polar molecule. Click here for Animation Click here for Animation In a polar molecules, the arrangement of atoms is such that the molecule has a permanent dipole moment because of charge separation. Water molecule is an example of a polar molecule. When a non-polar molecule is put in an electric field, the electric forces cause a small separation of the charges. The molecule thereby acquires an induced dipole moment. A polar molecule, which has a dipole moment in the absence of the electric field, gets its dipole moment aligned in the direction of the field. In addition, the magnitude of the dipole moment may also increase because of increased separation of the charges. Click here for Animation Conductor in an Electric Field Consider what happens when a conductor is placed in an electric field, say, between the plates of a parallel plate capacitor.Read More

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