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DC CIRCUITPREPARED BY:
130400116023- Patel Nidhi Harkishnbhai
130400116036- Sharma Surabhi Chandra Deo
BE First Semester IT
ACTIVE LEARNING ASSIGNMENTS
DEPARTMENT OF ELECTRICAL ENGINEERINGSANKALCHAND PATEL COLLEGE OF
ENGINEERING,VISNAGAR
Guided BY: Prof. P. R. Bhavsar
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DC Circuits
yThe circuityResistance in combinations
yKirchhoff’s RulesyRC transient circuits
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dq
dWε
Work done by a battery on charge
Here AB εε
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Real Battery and Single Loop circuits… What’s the current ?
Conservation of energy: Kirchoff’s first Law: Sum of voltages in a closed loop is zero.
2)( RrR
RiP
Rri
0iRir
ViRirV
2
2
R
aa
Real Circuit with ammeter and voltmeter
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Equivalent ResistanceResistors in Series
Series requirements– Conservation of energy– Potential differences add– Current is constant
n21 VVVV ...Apply Ohm’s Law to each resistor
n21eq IRIRIRIR ...
n21eq RRRR ...
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Resistors in parallel
Parallel requirements– Charge conservation– Currents must add– Potential difference is
same across each resistor
321 iiii
Apply Ohm’s Law to each resistor
n21eq RV
RV
RV
RV
...n21eq R1
R1
R1
R1
...
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Example 1
What is current through battery?
What is current through i2 ?
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Kirchhoff’s Rules1 The algebraic sum of the
currents entering a junction is zero. (Conservation of Charge)
2 The algebraic sum of the changes in electric potential difference around any closed circuit loop is zero. (Conservation of Energy)
Signs for Rule 2The direction of travel when traversing the loop is from a to b.
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Problem 2
Find the currents in each of the three legs of the circuit,
321 i,i,i
Three unknowns, need three equations. Also since batteries are in there cannot reduce the resistances since none in parallel or series
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Example: Applying Kirchhoff’s Rules
Apply Kirchhoff’s first rule to the three wire junction at the bottom of the diagram
0III 312
Apply Kirchhoff’s second rule to the closed path in red, traversing it clockwise
0I05I03V05 21 ...
Apply Kirchhoff’s second rule to the closed path in green, traversing it clockwiseNote the sign changes for some of the elements
0I07V010I03V05 31 ....
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Another, example: applying Kirchhoff’s Rules
Solve the equations simultaneously for the values if I. If I is negative the current is in the opposite direction
0III 312
0I05I03V05 21 ...
0I07I03V05 31 ...
A7740I
A9150I
A1410I
3
2
1
.
.
.
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RC Circuits and Time dependence
Time dependence
Resistor slows down the charging of the capacitor
Time dependent behavior (transient) 2 cases: switch at
“a” or at “b”
a) Chargingb) discharging
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In position “a” Charging the Capacitor
Use Kirchhoff’s Loop rule
Or the voltage across capacitor is …..
RCt
c
RCt
R
e1V
e1Cq
RRC
q
dt
dq
0IRq
0VV
(t)
(t)
(t)(t)
C-
- c
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What’s VR across resistor?Find the current and multiply by R
,or ....
get and derivative take
(t)
(t)
(t)
(t)
1(t)
RCt
R
RCt
RCt
e
Rdt
dqV
eR
I
dt
dqI
eCq
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RCt
0c
RCt
0
RCt
0
R
eVV
eCVeqq
RC
q
dt
dq
0VV
(t)
(t)
(t)(t)
c
Discharging Position b:
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1. Charging the Capacitor
Note: RCis called the time constant