Formula Sheets: DC Circuit | Basic Electrical Technology - Electrical Engineering (EE) PDF Download

 Page 1


Formula Sheet for DC Circuits (Basic Electrical
Technology) – GATE
1. Basic Concepts
• DC Circuit: Circuit with constant voltage and current (no time-varying signals).
• Charge: Q=It, where Q: Charge (C), I: Current (A), t: Time (s).
• Current: I =
dQ
dt
, ?ow of electric charge.
• Voltage: Potential di?erence, V =
W
Q
, where W: Work (J).
2. Ohms Law
• Ohms Law:
V =IR
where V: Voltage (V), I: Current (A), R: Resistance (? ).
• Conductance:
G=
1
R
where G: Conductance (S).
3. Power and Energy
• Power:
P =VI =I
2
R=
V
2
R
where P: Power (W).
• Energy:
W =Pt=VIt
where W: Energy (J), t: Time (s).
4. Kirchho?s Laws
• Kirchho?s Current Law (KCL): Sum of currents entering a node equals sum
of currents leaving:
?
I
in
=
?
I
out
• Kirchho?s Voltage Law (KVL): Sum of voltage drops around a closed loop is
zero:
?
V =0
1
Page 2


Formula Sheet for DC Circuits (Basic Electrical
Technology) – GATE
1. Basic Concepts
• DC Circuit: Circuit with constant voltage and current (no time-varying signals).
• Charge: Q=It, where Q: Charge (C), I: Current (A), t: Time (s).
• Current: I =
dQ
dt
, ?ow of electric charge.
• Voltage: Potential di?erence, V =
W
Q
, where W: Work (J).
2. Ohms Law
• Ohms Law:
V =IR
where V: Voltage (V), I: Current (A), R: Resistance (? ).
• Conductance:
G=
1
R
where G: Conductance (S).
3. Power and Energy
• Power:
P =VI =I
2
R=
V
2
R
where P: Power (W).
• Energy:
W =Pt=VIt
where W: Energy (J), t: Time (s).
4. Kirchho?s Laws
• Kirchho?s Current Law (KCL): Sum of currents entering a node equals sum
of currents leaving:
?
I
in
=
?
I
out
• Kirchho?s Voltage Law (KVL): Sum of voltage drops around a closed loop is
zero:
?
V =0
1
5. Series and Parallel Circuits
• Resistors in Series:
R
eq
=R
1
+R
2
+···+R
n
• Resistors in Parallel:
1
R
eq
=
1
R
1
+
1
R
2
+···+
1
R
n
• Two Resistors in Parallel:
R
eq
=
R
1
R
2
R
1
+R
2
• Voltage Division:
V
R
k
=V
total
R
k
R
1
+R
2
+···+R
n
• Current Division (Two Resistors):
I
R
1
=I
total
R
2
R
1
+R
2
6. Source Transformations
• Voltage to Current Source:
I
s
=
V
s
R
, R in parallel
• Current to Voltage Source:
V
s
=I
s
R, R in series
7. Network Theorems
• Superposition Theorem: Total response is the sum of responses due to each
independent source acting alone.
• Thevenins Theorem: Any linear network can be replaced by a voltage sourceV
th
in series with resistance R
th
.
V
th
= Open-circuit voltage, R
th
=
V
oc
I
sc
• Nortons Theorem: Any linear network can be replaced by a current source I
n
in
parallel with resistance R
n
.
I
n
= Short-circuit current, R
n
=R
th
• Maximum Power Transfer Theorem: Maximum power delivered to load when
R
load
=R
th
.
P
max
=
V
2
th
4R
th
2
Page 3


Formula Sheet for DC Circuits (Basic Electrical
Technology) – GATE
1. Basic Concepts
• DC Circuit: Circuit with constant voltage and current (no time-varying signals).
• Charge: Q=It, where Q: Charge (C), I: Current (A), t: Time (s).
• Current: I =
dQ
dt
, ?ow of electric charge.
• Voltage: Potential di?erence, V =
W
Q
, where W: Work (J).
2. Ohms Law
• Ohms Law:
V =IR
where V: Voltage (V), I: Current (A), R: Resistance (? ).
• Conductance:
G=
1
R
where G: Conductance (S).
3. Power and Energy
• Power:
P =VI =I
2
R=
V
2
R
where P: Power (W).
• Energy:
W =Pt=VIt
where W: Energy (J), t: Time (s).
4. Kirchho?s Laws
• Kirchho?s Current Law (KCL): Sum of currents entering a node equals sum
of currents leaving:
?
I
in
=
?
I
out
• Kirchho?s Voltage Law (KVL): Sum of voltage drops around a closed loop is
zero:
?
V =0
1
5. Series and Parallel Circuits
• Resistors in Series:
R
eq
=R
1
+R
2
+···+R
n
• Resistors in Parallel:
1
R
eq
=
1
R
1
+
1
R
2
+···+
1
R
n
• Two Resistors in Parallel:
R
eq
=
R
1
R
2
R
1
+R
2
• Voltage Division:
V
R
k
=V
total
R
k
R
1
+R
2
+···+R
n
• Current Division (Two Resistors):
I
R
1
=I
total
R
2
R
1
+R
2
6. Source Transformations
• Voltage to Current Source:
I
s
=
V
s
R
, R in parallel
• Current to Voltage Source:
V
s
=I
s
R, R in series
7. Network Theorems
• Superposition Theorem: Total response is the sum of responses due to each
independent source acting alone.
• Thevenins Theorem: Any linear network can be replaced by a voltage sourceV
th
in series with resistance R
th
.
V
th
= Open-circuit voltage, R
th
=
V
oc
I
sc
• Nortons Theorem: Any linear network can be replaced by a current source I
n
in
parallel with resistance R
n
.
I
n
= Short-circuit current, R
n
=R
th
• Maximum Power Transfer Theorem: Maximum power delivered to load when
R
load
=R
th
.
P
max
=
V
2
th
4R
th
2
8. Mesh and Nodal Analysis
• Mesh Analysis: Apply KVL to each mesh:
?
V =
?
I
k
R
k
• Nodal Analysis: Apply KCL at each node:
?
I =
?
V
node
-V
k
R
k
9. Capacitors and Inductors in DC
• Capacitor in Steady-State DC: Acts as open circuit.
I
C
=0, V
C
= constant
• Inductor in Steady-State DC: Acts as short circuit.
V
L
=0, I
L
= constant
10. Design Considerations
• Circuit Simpli?cation: Use series/parallel combinations and source transforma-
tions.
• Power Rating: Ensure resistors and components can handle power dissipation.
• Applications: Power supplies, battery circuits, control systems.
• Analysis Techniques: Choose mesh/nodal analysis or theorems based on circuit
complexity.
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