Circuits

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CHAPTER-27

• Circuits

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Ch 27-2 Pumping Charges

• Charge Pump
• A emf device that maintains steady flow of
  charges through the resistor.
• Emf device does work on charge carrier by doing
  work
• Within the emf device , positive charge carrier
  moves from negative terminal (a region of low
  electric potential energy) to positive terminal
  (a region of high electric potential energy)
  against E field inside the device.
• This energy ?, which is chemical energy , is
  supplied by emf device
• ?amount of work dW/charge dq

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Ch 27-3 Work, Energy, and Emf

• Circuit containing two batteries
• For a circuit with two emf with similar terminal
  connected net emf in the circuit is difference of
  the two emf and net current direction in the
  direction of the stronger emf.
• For a circuit with two emf with opposite terminal
  connected net emf in the circuit is sum of the
  two emf and net current direction in the
  direction of the any of the emf.

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Ch 27-4 Calculating the Current in a Single-Loop
Circuit

• Energy Method
• A current i passes through the resistor R for a
  time dt sec. Charge dqidt passes through the
  resistor.
• Work done by battery to move this charge through
  the resistor dW?dq ?idt
• His work must be equal to thermal energy
  dissipated in the resistor ?idti2Rdt
• ?iR and i ?/R
• Potential Method
• Potential method involve calculating the
  potential difference between two points ?VVf-Vi
  when you move in a circuit
• If you move in a circuit clockwise or
  anticlockwise in a loop the ViVf
• ?V0

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Ch 27-4 Calculating the Current in a Single-Loop
Circuit

• Kirchoffs Loop Rule
• Algebric sum of potential drop ?V encountered in
  a complete traversal of any loop is zero i.e
• For a loop ? ?Vi0
• Resistance Rule
• For a move through the resistance R along
  direction of current i potential drop ?V -iR
• For a move through resistance R in direction
  opposite to current i potential drop ?V iR
• EMF Rule
• For a move through emf device along direction of
  emf arrow potential drop ?V ?
• For a move through emf device opposite to
  direction of emf arrow potential drop ?V -?

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Ch 27-4 Calculating the Current in a Single-Loop
Circuit

• Potential Method
• Moving in the circuit clock wise from point a
• ?V? -iR0
• ? iR and i ?/R

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Ch 27-5 Other Single-Loop Circuit

• Battery Internal Resistance
• Electrical resistance of the battery conducting
  material , shown with resistance r in series with
  emf ?
• Resistance in Series Resistance in series can be
  represented by an equivalent resistance Req given
  by
• Req ? Ri

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Ch 27-6 Potential Difference between two points

• To find potential difference between any two
  points in a circuit, start at one point and
  traverse the circuit to the other point ,
  following any path and add algebraically the
  changes in potential you encounter
• To calculate potential difference Vb-Va start at
  a then
• Va ?-ir Vb then
• Vb-Va V ?-ir
• A current I through a circuit containing a
  battery with internal resistance r and an
  external resistor R is i?/(rR)
• Vb-Va V ?-ir ?-r?/(rR) ?R/(Rr)

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Ch 27-6 Potential Difference between two points

• Grounding a Circuit
• Connecting the circuit to a conducting path to
  Earth. The potential at the grounding point is
  defined to be Zero.

• Power, potential and Emf
• When a emf device does work to establish a
  current i in the circuit, the device transfers
  its chemical energy to the charge carrier. It
  loses power in its internal resistance r.
• Energy transfer rate P from emf to charge carrier
• P iVi(?-ir)i?-i2r
• Pri2r (internal dissipation rate)
• Pemf i?

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Ch 27-7 Multiloop Circuits

• Junction rule
• The sum of currents entering the junction must be
  equal to the currents leaving the junction
• Resistance in Parallel
• The resistance connected in parallel have common
  voltage
• Resistance in parallel can be represented by an
  equivalent resistance Req given by
• 1/Req 1/? Ri

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Ch 27-8 Ammeter and Voltmeter

• Ameter A connected in series while voltmeter V is
  used in Paralell.
• If RA is internal resistance of an ammeter and RV
  is internal resistance of a voltmeter then
• RA should be very small
• RV should be very large

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Ch 27-9 RC Circuits

• Charging the capacitor-time varying current
• In switch position a current flows through the
  resistor R and charge q start building up on the
  capacitor plate. The capacitor voltage V q/C.
• For fully charged capacitor no current flows
  through the resistor and voltage V across the
  capacitor is ? then qC?.
• During charging process the loop rule to the
  circuit gives
• ? - iR-q/C0 ? Rdq/dtq/C
• qC?(1-e-t/RC)
• Current idq/dt (?/R) e-t/RC
• Voltage Vq/c?(1-e-t/RC)
• Time constant ?RC
• qC?(1-e-t/RC)C?(1-e-1)0.63 C?

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Ch 27-9 RC Circuits

• Discharging a capacitor
• In switch position b the charging equation
• ? Rdq/dtq/C reduces to
• 0 Rdq/dtq/C (? 0)
• Then qq0e-t/RC and q0CV0
• idq/dt-(q0/RC)e-t/RC-i0e-t/RC