**a.**

Since all the bulbs are identical, we take the resistance of each bulb to be R.

Power is expressed as:

$\overline{){\mathbf{P}}{\mathbf{=}}{{\mathbf{i}}}^{{\mathbf{2}}}{\mathbf{R}}}$

From this equation, the current is directly proportional to power.

Ohm's law:

$\overline{){\mathit{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

We need to determine the current flowing in each branch.

Let's re-label the figure as below.

The currents are drawn based on Kirchhoff's junction rule.

The circuit shown has four identical light bulbs and an ideal battery

a. Rank the brightness of the bulbs. Explain your reasoning.

b. A wire is now added to the circuit as shown.

i. Does the brightness of bulb C increase, decrease or remain the same? Explain your reasoning.ii. Does the brightness of bulb A increase, decrease, or remain the same? Explain.

iii. Does the current through the battery increase, decrease, or the remain the same? Explain.

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