Question

Using Norton's theorem, calculate the current flowing through the 15 ohm load
resistor in the circuit.​

Answer 1

Answer:

Using Norton's theorem, calculate the current flowing through the 15 ohm load

resistor

Answer 2

Concept:

According to Norton's Theorem, a single constant current generator connected in parallel with a single resistor can replace any linear circuit made up of several energy sources and resistances.

Given:

An electrical circuit with four resistors of resistance $4,6,8,15$ ohms and an ammeter with reading $4A$ and battery with voltage as $30V$.

Find:

the current flowing through $15$ ohm resistor.

Solution:

Let the current from the battery be $I$ and the current flowing through the resistor $R_L$ be $I_1$.

Then the current in CD will be $I-I_1$.

Now by using the Nortons theorem,

The current equation,

$I-I_1=4$

The voltage equations:

$4I+6I_1=30$

Solving these two equations we get,

$I=5.4A$

$I_1=1.4A$

Replacing the different energy sources with a single source and single resistor.

The Nortons current, $I_N=I_1=1.4A$

Norton's resistor $R_N$ is:

$=6+15=21ohm$

$\frac{1}{r_1}=\frac{1}{8}+\frac{1}{21} \\r_1=6\Omega$

So,

$R_N=6+4=10\Omega$

The current through the 15-ohm resistor.

$I_L=\frac{I_N\times R_N}{R_N+R_L}$

$I_L=\frac{1.4\times 10}{10+15}$

$I_L=0.56A$

The current flowing through 15-ohm load resistor is $0.56A$.

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