Assumed Direction of Current:
In applying Kirchhoff's laws to electrical networks, the direction of current flow may be
assumed either clockwise or anticlockwise. If the assumed direction of current is not the actual
direction, then on solving the question, the current will be found to have a minus sign.
If the answer is positive, then assumed direction is the same as actual direction.
However, the important point is that once a particular direction has been assumed, the same
should be used throughout the solution of the question.
Kirchhoff's laws are applicable both to d.c. and a.c. voltages and currents. However, in the case
of alternating currents and voltages, any e.m.f. of self-inductance or that existing across a
capacitor should be also taken into account.
ELECTRICAL CIRCUITS
EEE
MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY
VOLTAGE-CURRENT RELATIONSHIPS FOR PASSIVE ELEMENTS
The Three Passive Elements are Resistance, Inductance and Capacitance. The behavior of these three elements along
with the respective voltage-current relationship is given in the table.
Element
Basic Relation
Voltage across, If Current Known
Current through, If Voltage Known
R
R=
𝑉
𝐼
V
R
(t)=R i
R
(t)
i
R
(t)=
V
R
(t)
𝑅
L
L=
𝑁∅
𝐼
V
L
(t)=L
𝑑𝑖(𝑡)
𝑑𝑡
i
L
(t)=
1
𝐿
∫
𝑉(𝑡)𝑑𝑡
𝑡
−∞
C
𝐶 =
𝑄
𝑉
V
C
(t)=
1
𝐶
∫
𝑖
𝐶
(𝑡)𝑑𝑡
𝑡
−∞
i
C
(t)=C
𝑑𝑣(𝑡)
𝑑𝑡
Table
1.
A current waveform flowing through an inductor of 1mH is shown in the figure. Obtain and sketch the waveform
of voltage across the inductor.
Solution:
From the given waveform,
For 0Therefore, i(t)=50t and
𝑑𝑖(𝑡)
𝑑𝑡
=50
For 2𝑑𝑖(𝑡)
𝑑𝑡
=0
For 4Therefore, i(t)=-50t and
𝑑𝑖(𝑡)
𝑑𝑡
=-50
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