By Kirchhoff's junction rule:

I = I_{1} - I_{2}

By Kirchhoff's loop rule:

In the upper loop

$\begin{array}{rcl}{\mathbf{\epsilon}}_{\mathbf{1}}\mathbf{-}{\mathbf{I}}_{\mathbf{1}}{\mathbf{r}}_{\mathbf{1}}\mathbf{-}{\mathbf{I}}_{\mathbf{2}}{\mathbf{r}}_{\mathbf{2}}\mathbf{-}{\mathbf{\epsilon}}_{\mathbf{2}}\mathbf{-}{\mathbf{I}}_{\mathbf{1}}\mathbf{R}& \mathbf{=}& \mathbf{0}\\ \mathbf{13}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{025}{\mathbf{I}}_{\mathbf{1}}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{02}{\mathbf{I}}_{\mathbf{2}}\mathbf{-}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{2}{\mathbf{I}}_{\mathbf{1}}& \mathbf{=}& \mathbf{0}\end{array}$

8 = 0.225I_{1} + 0.02I_{2}

In the lower loop:

The circuit diagram below shows two emf sources and a bulb connected in parallel. Also connected in the circuit is a resistor with resistance R = 0.2Ω. The resistance of the bulb is R_{b} = 0.5 Ω , and each of the sources has internal resistance: r_{1} = 0.025 Ω and r_{2} = 0.02 Ω.

If ε_{1} = 13.0 V and ε_{2} = 5.0 V ,

Part A. Calculate the current I_{2} flowing in emf source ε_{2}

Part B

Calculate the current I_{1} flowing in emf source ε_{1}.

Express your answer in amperes to three significant figures.

Part C

A useful strategy to evaluate your answer is to consider a loop other than the ones you used to solve the problem; if the sum of potential drops around this loop isn’t zero, you made an error somewhere in your calculations. Begin by calculating the current I_{1} flowing through the emf source ε_{1}.

Express your answer in amperes to three significant figures.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

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