Question

Consider the figure below. The current through 6 ohm resistor is 4A in the direction shown. What are the currents through the 25 ohm and 20 ohm resistors? ​

Answer 1

Answer:

The current through 25 Ω resistor is 7 A

The current through 20 Ω resistor is 9.95 A

Explanation:

Let the current through 6 Ω, 8 Ω, 25 Ω, and 20 Ω resistors be $I_6$, $I_8$, $I_{25}$, and $I_{20}$ respectively.

$I_6$ = 4 A

Then the voltage across that resistor can be found out using the relation

$V = I R$ where I is the current and R is the resistance.

Thus the voltage across the 6 Ω resistor is

$V_6$ = 6 × 4 = 24 v

The voltage across the 8 Ω resistor is the same as that of the 6 Ω resistor. So, we can find the current through the 8 Ω resistor

$I_8$ = $\frac{24}{8}$ = 3 A

The current through the 25 Ω resistor is the sum of the currents $I_6$ and $I_8$.

i.e. $I_{25}$ = 4 + 3 = 7 A

The effective resistance of the top branch can be found out as

$R_{T}$ = $\frac{8 \times 6}{8 + 6} + 25 = \frac{48}{14} + 25 = 3.43 + 25$

     = 28.43 Ω

Then the current through 20 Ω resistor can be found out as

$I_{20} = 7 \times \frac{28.43}{20}$

$I_{20}$ = 9.95 A

The current through 25 Ω resistor is 7 A

The current through 20 Ω resistor is 9.95 A

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