Find the current flow?

Electricity and Magnetism Level 2

In the circuit shown, the source E 0 E_0 has a voltage of 5 V \text{5 V} and internal resistance of r = 0.1 Ω r = 0.1\ \Omega , resistances of R 1 R_1 and R 2 R_2 are 4 Ω 4\ \Omega and 6 Ω 6\ \Omega respectively. Find the currents through R 1 R_1 and R 2 R_2 respectively.

1.2 A, 0.8 A 1.7 A, 1.8 A 3.1 A, 3.9 A 6.2 A, 6.5 A 1.8 A, 1.7 A None of the others 1.6 A, 1.5 A 1.9 A, 1.7 A

Nnsv Abhiram by Nnsv Abhiram , 16, India

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2 solutions

The equivalent circuit is as shown. Then we have:

I = E 0 r + R 1 ∣ ∣ R 2 = 5 0.1 + 4 ∣ ∣ 6 = 5 0.1 + 4 × 6 4 + 6 = 2 A \begin{aligned} I & = \frac {E_0}{r + R_1||R_2} = \frac {5}{0.1+4||6} = \frac {5}{0.1 + \frac {4\times 6}{4+6}} = 2 \text{ A} \end{aligned}

Using current division:

{ I 1 = R 2 R 1 + R 2 I = 6 4 + 6 × 2 = 1.2 A I 2 = R 1 R 1 + R 2 I = 4 4 + 6 × 2 = 0.8 A \begin{cases} I_1 = \dfrac {R_2}{R_1+R_2} I = \dfrac {6}{4+6} \times 2 = 1.2 \text{ A} \\ I_2 = \dfrac {R_1}{R_1+R_2} I = \dfrac {4}{4+6} \times 2 = 0.8 \text{ A} \end{cases}

Therefore, the answer is 1.2 A, 0.8 A \boxed{\text{1.2 A, 0.8 A}} .

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thanks for changing image

Nnsv Abhiram - 2 years, 3 months ago

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Learn up LaTex since you like to post problems.

Chew-Seong Cheong - 2 years, 3 months ago
Nnsv Abhiram
Mar 4, 2019

Let the current flows in R {1} is I {1} And current flows in R {2} is I {2} then the respective formulas will be :

Therefore,the answers are 1.2 and 0.8.

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@Nnsv Abhiram Learn up LaTex since you like to post problems.

chakravarthy b - 2 years, 3 months ago

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