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CURRENT ELECTRICITY

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Hertz Experiment: Induction Coil Copperor Zinc Plate Metal Rod Metal Rod Metal Spheres Ring P P S S EM Wave Copper or Zinc Plate The copper or zinc plates are kept parallel separated by 60 cm. The metal spheres are slided over the metal rods to have a gap of 2 to 3 cm. Induction coil supplies high voltage of several thousand volts. The plates and the rods (with spheres) constitute an LC combination. An open metallic ring of diameter 0.70 m having small metallic spheres acts as a detector. This constitutes another LC combination whose frequency can be varied by varying its diameter. S1 S2 S1 ’ S2 ’

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CURRENT ELECTRICITY -2 Internal resistance of a cell  Cells in series and parallel  Kirchhoff’s Rules  Wheatstone’s bridge  Metre bridge  Potentiometer  Comparison of emf using potentiometer  Internal resistance of a cell using potentiometer

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S. No. EM Wave Rangeof λ Range of ν Source Use 5 Ultra Violet Rays 3.8 x 10-7 m to 6 x 10-10 m 8 x 1014 Hz to 3 x 1017 Hz Atoms and molecules in electrical discharges and Sun Medical application, sterilization, killing bacteria and germs in food stuff, detection of invisible writing, forged documents, finger print, etc. 6 X - Rays 10-9 m to 6 x 10-12 m 3 x 1017 Hz to 5 x 1019 Hz Inner or more tightly bound electrons in atoms X-ray photography, treatment of cancer, skin disease & tumor, locating cracks and flaws in finished metallic objects, detection of smuggled goods in bags of a person, study of crystal structure, etc. 7 γ-Rays They overlap the upper limit of the X- Ray. 10-10 m to 10-14 m 3 x 1018 Hz to 3 x 1022 Hz Radioactive substances Information about structure of nuclei, astronomical research, etc. End of EM Waves

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Properties of ElectromagneticWaves: 0 X E0 B0 Y Z 1. Variations in both electric and magnetic fields occur simultaneously. Therefore, they attain their maxima and minima at the same place and at the same time. 2. The direction of electric and magnetic fields are mutually perpendicular to each other and as well as to the direction of propagation of wave. 3. The electric field vector E and magnetic field vector B are related by c = E0 / B0 where E0 and B0 are the amplitudes of the respective fields and c is speed of light.

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Properties of ElectromagneticWaves: 0 X E0 B0 Y Z 1. Variations in both electric and magnetic fields occur simultaneously. Therefore, they attain their maxima and minima at the same place and at the same time. 2. The direction of electric and magnetic fields are mutually perpendicular to each other and as well as to the direction of propagation of wave. 3. The electric field vector E and magnetic field vector B are related by c = E0 / B0 where E0 and B0 are the amplitudes of the respective fields and c is speed of light.

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Internal Resistance ofa cell  The electromotive force (emf), E, is the potential difference between the positive and negative electrodes in an open circuit(ie) when no current is flowing through the cell.  The electrolyte through which the current flows has a finite resistance r, called the internal resistance.  The terminal potential difference, V is the potential difference between the terminals of the cell when current is flowing through the cell. V= E –Ir According to ohm’s law, V=IR Therefore, IR=E-Ir I= 𝐸 𝑅+𝑟 The max current that can be drawn from a cell is 𝐼𝑚𝑎𝑥 = 𝐸 𝑟 (for R=0)

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Internal resistance ofa cell in terms of E,V & R V=E-Ir Ir= E-V Dividing by IR=V, 𝐼𝑟 𝐼𝑅 = 𝐸 − 𝑉 𝑉 ⇒ 𝑟 = 𝐸 𝑉 − 1 𝑅

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Cells in Series Considertwo cells of emf 𝐸1 𝑎𝑛𝑑 𝐸2, of internal resistances 𝑟1 𝑎𝑛𝑑 𝑟2 respectively, joined in series. Using the relation for potential difference and internal resistance, 𝑉 𝑒𝑞 = 𝑉1 + 𝑉2 = 𝐸1 − 𝐼𝑟1 + 𝐸2 − 𝐼𝑟2 𝑉 𝑒𝑞 = 𝐸𝑒𝑞 − 𝐼𝑟𝑒𝑞 = 𝐸1 + 𝐸2 + 𝐼(𝑟1+𝑟2)  The equivalent emf, 𝐸𝑒𝑞=𝐸1 + 𝐸2  The effective resistance of the combination, 𝑟𝑒𝑞 =𝑟1 + 𝑟2

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Extending to nnumber of cells in series combination : (i) The equivalent emf of a series combination of n cells is just the sum of their individual emfs. (ii) The equivalent internal resistance of a series combination of n cells is just the sum of their internal resistances.

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(ii) Cells inparallel combination Consider two cells of emf 𝐸1 𝑎𝑛𝑑𝐸2, of internal resistances 𝑟1 and 𝑟2 respectively combined in parallel 𝐼2= 𝐼 − 𝐼1 The current in the external circuit is divided among the cells. 𝐼 = 𝐼1 + 𝐼2 = 𝐸1−𝑉 𝑟1 + 𝐸2−𝑉 𝑟2 = ( 𝐸1 𝑟1 + 𝐸2 𝑟2 ) − 𝑉( 1 𝑟1 − 1 𝑟2 )

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𝑉 𝑒𝑞 = 𝐸𝑒𝑞− 𝐼𝑟𝑒𝑞 = 𝐸1𝑟2+𝐸2𝑟1 𝑟1+𝑟2 - I( 𝑟1𝑟2 𝑟1+𝑟2 ) ⇒ 1 𝑟𝑒𝑞 = 1 𝑟1 + 1 𝑟2 ⇒ 𝐸𝑒𝑞 𝑟𝑒𝑞 = 𝐸1 𝑟1 + 𝐸2 𝑟2 For n no. of cells in parallel combination,  1 𝑟𝑒𝑞 = 1 𝑟1 + 1 𝑟2 +. . … + 1 𝑟𝑛  𝐸𝑒𝑞 𝑟𝑒𝑞 = 𝐸1 𝑟1 + 𝐸2 𝑟2 +. . … + 𝐸𝑛 𝑟𝑛

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KIRCHHOFF’S RULES (I)Junction rule: At any junction , the sum of the currents entering the junction is equal to the sum of the currents leaving the junction. 𝐼1 + 𝐼2 + 𝐼3 = 𝐼4 + 𝐼5 Sign convention 1. The currents coming into the junction is taken as positive. 2. The currents leaving the junction is taken as negative. When currents are steady, there is no accumulation of charges at any junction or at any point in a line.

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(II)Loop rule:  Thealgebraic sum of changes in potential around any closed loop involving resistors and cells in the loop is zero Or The algebraic sum of all the potential drops and emfs along any closed path in an electrical network is always zero. Sign Conventions (i) The emf is taken negative when we traverse from positive to negative terminal of the cell through the electrolyte. (ii) The emf is taken positive when we traverse from negative to positive terminal of the cell through the electrolyte.

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 Using Kirchhoff’sjunction rule the current direction and values are marked  Using Kirchhoff’s loop rule , For loop AFCBA +𝐸1 − 𝐼1 + 𝐼2 𝑅1 − 𝐼1 + 𝐼2 𝑅2 − 𝐼1𝑅5=0 For loop EDCFE, −𝐸2+ 𝐼1 + 𝐼2 𝑅1 + 𝐼1 + 𝐼2 𝑅2 + 𝐼2𝑅4 + 𝐼2𝑅3=0

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Wheatstone Bridge The Wheatstonebridge has four resistors P,Q,R and X. The arm AC is called the battery arm. The arm BD is called the galvanometer arm. Current flows through all the resistors and 𝐼𝑔 is the current flowing through the galvanometer. In a balanced bridge, the resistors are such that 𝐼𝑔 = 0 Applying Kirchhoff's rule to the closed loops ABDA and CBDC, For loop ABDA -𝐼1𝑃 + 𝐼2𝑅 = 0 𝐼1 𝐼2 = 𝑅 𝑃 For loop BCDB, -𝐼1𝑄 + 𝐼2𝑋 = 0 Therefore, 𝐼1 𝐼2 = 𝑋 𝑄 From the above equation, 𝑃 𝑄 = 𝑅 𝑋

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Potentiometer  It isa long piece of uniform wire of a few metres in length, fixed on a wooden board, across which a standard cell is connected  Principle: If a constant current flows through a wire of uniform cross section, then the potential difference across any length of the wire is directly proportional to its length.

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Comparison of emf’susing potentiometer  Two cells of emf𝐸1 𝑎𝑛𝑑 𝐸2 are connected as shown in the circuit to a potentiometer. The balance point is obtained for the cells 𝐸1 𝑎𝑛𝑑 𝐸2 separately,(say 𝑙1&𝑙2respectively ) ,where the potential at the point on the potentiometer wire is equal and opposite to the emf of the cell 𝐸1 = ϕ𝑙1 = 𝐼ρ𝑙1 𝐴 𝐸2 = ϕ𝑙2 = 𝐼ρ𝑙2 𝐴 𝐸1 𝐸2 = 𝑙1 𝑙2

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