First slide

Cell

Question

In the circuit shown below E₁ = 4.0 V, $R_{1} = 2 Ω, E_{2} = 6.0 V, R_{2} = 4 Ω, and R_{3} = 2 Ω$ current I₁ is :

Moderate

A

1.6 A
B

1.8 A
C

1.25 A
D

1.0 A

Solution

$\begin{array}{l} \frac{1}{r_{e l}} = \frac{1}{4} + \frac{1}{2} \\ r_{e q} = 4 / 3 Ω \\ E_{e q} = (\frac{ε_{1}}{r_{1}} + \frac{ε_{2}}{r_{2}}) r_{e q} \\ = (\frac{6}{4} + \frac{0}{2}) (4 / 3) = 2 V \\ I_{1} = \frac{4 V + E_{e q}}{2 Ω + r_{e q}} \\ = (\frac{4 + 2}{2 + 4 / 3}) A = 1 .8 A \end{array}$

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