Lecture%206%20Direct%20Current%20Circuits

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Lecture 6Direct Current Circuits
Chapter 18
Outline

• Energy Source in Circuits
• Resistor Combinations
• Kirchhoffs Rules
• RC Circuits

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Energy in Circuits
Direct current is a current flowing in one
direction through a circuit.
Circuits are usually powered by batteries or
generators, which are called sources of emf. The
emf (E)stands for electromotive force and is not
a fundamental force. E is the work per unit
charge and is measured in volts (V).
E equals to the potential difference across the
battery if the batterys internal resistance is
neglected.
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Emf and Circuit Parameters
?V E ? IRint
?V IRload
E IRload IRint
E I ???? Rload Rint
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Emf
E is equal to the terminal voltage in the absence
of the current.
EI I2Rload I2Rint

• The total power output of the source of emf is
  converted to
• the power delivered to the load resistance
• the power delivered to the internal resistance

In all the problems, we assume that the internal
resistance of the battery is negligible.
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Resistors in Series
The current (I) is the same in both
resistors. ?V1 IR1, ?V2IR2
?V IR1 IR2 I(R1R2)
?V IReq
Req R1 R2
Example
The equivalent resistance of a series combination
of resistors equals to the algebraic sum of the
individual resistances.
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Resistors in Parallel
The potential differences across both resistors
are the same (?V), as each is directly connected
to the battery.
Due to conservation of charge, Itot I1 I2
?V ?V ?V
1 1 1 Itot ?? I1 I2 ?? ??
? ? ? ? Req
R1 R2 Req R1 R2
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Kirchhoffs Rules
Circuit elements can be connected in various
ways. For analysis of complex circuits, 2 rules
proposed by Gustav Kirchhoff in 1845 can be
applied.

1. The sum of all the currents entering any junction
   point is equal to the sum of all the currents
   leaving that junction point (junction rule).
2. The sum of the potential differences across all
   the elements around any closed-circuit loop must
   be zero (loop rule).

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Kirchhoffs rules
The junction rule is a consequence of
conservation of charge, the loop rule is a
consequence of conservation of energy.
Application of Kirchhoffs rules
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RC Circuits
Circuits which contain capacitors have
time-dependent currents.
Q and E are the maximum charge and voltage across
the capacitor C is the capacitance
Q CE
q(t) Q(1 ? e?t/RC) e 2.718 ? RC is the
capacitors time constant
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RC Circuits
Another view of a RC circuit
Problem An uncharged capacitor and a resistor
are connected in a series to an emf source. E
10 V, C 20 ?F, R 100 ?. Find the circuits
time constant, the maximum charge on the
capacitor, the charge on the capacitor after 1
time constant.
Solution ? RC (102 ?) (2 10?5 F) 2 10?3
c Q CE (2 10?5 F) (10 V) 2 10?4 C 200
?C q 0.632 Q 0.632 (200 ?C) 126 ?C
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Summary

• Direct current is current that flow in a circuit
  in one direction
• Kirchhoffs rules are a set of instructions to
  analyze complex circuits. The rules are
  consequences of conservation of charge and
  energy.
• Circuits containing capacitors have
  time-dependent currents. The charge on the
  capacitor and time dependence of the current
  through it can be determined using the capacitor
  time constant.