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1.Find the current in the 3.00 Ω resistor. (Note that three currents are given.)
2.Find the unknown emfs ε1 and ε2.
3.Find the resistance R .
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Kirchhoff’s junction rule and Ohm’s law are the concepts that will solve this problem.
First, from the given currents, find the current in the
resistor. Find the unknown emfs using Kirchhoff’s voltage law. Similar to the Kirchhoff voltage law, you can find the unknown resistance.
Ohm’s law says that the current between two points of a circuit is proportional the potential difference between them. The resistance is the constant of proportionality.
Kirchhoff’s circuit laws that govern current and voltage are used in electrical circuits. Kirchhoff’s current law says that the total amount of current entering a node is equal to its total output.
Kirchhoff’s voltage law says that the total voltage around closed loops is zero.
(26.23.1)
Below is a diagram showing the current direction through the circuit.
The current in the line
and in the line
combine and flow together through the line
as current
.
The current line
is given by
Here,
is the current in the line
and
is the current in the line
.
Substitute
for
and
for
to find the current
.
(26.23.2.1)
Kirchhoff’s voltage law is applied to loop
.
Substitute
for
to find the emf
.
The emf
is
(26.23.2.2)
Kirchhoff’s voltage law is applied to loop
.
Substitute
for
to find the emf
.
The emf
is
(26.23.3)
Kirchhoff’s voltage law is applied to loop
.
Substitute
for
and
for
to find the resistance
.
Ans: Part 26.3.1
The current in the
is
Part 26.23.2.1
The emf
is
Part 26.23.2.2
The emf
is
Part 26.23.3
The resistance
is
.