Question

how does a parallel circuit change when a branch is added? the total resistance increases, so the current in the circuit decreases. the total resistance decreases, so the current in the circuit increases. the total resistance increases, so bulbs shine at a lower brightness. the total resistance decreases, so bulbs shine at a higher brightness.

Explanation:

In a parallel - circuit, when a branch is added, more paths for current flow are available. According to the formula for equivalent resistance in parallel circuits $\frac{1}{R_{eq}}=\sum_{i = 1}^{n}\frac{1}{R_i}$, adding a branch (a new $R_i$) causes the equivalent resistance $R_{eq}$ to decrease. By Ohm's law $I=\frac{V}{R}$, with voltage $V$ constant, a decrease in resistance $R$ leads to an increase in current $I$. And the brightness of a bulb is related to the power $P = I^2R$ (for a bulb with fixed resistance). More current means more power and thus higher brightness.

Answer:

The total resistance decreases, so bulbs shine at a higher brightness.