Question

which statement below uses the choices from the graph below?
the smaller the slope of the line the greater the resistance.
voltage increases with current.
the bigger the slope of the line the greater the resistance.
an increase in current can result in greater voltage if more resistance is not added.

in the three circuits shown below, the batteries are all identical, and the light bulbs are all identical. in circuit 1, a single light bulb is connected to the battery. in circuits 2 and 3, two light bulbs are connected to the battery in different ways, as shown. the lightbulbs are labeled a - e.
rank the magnitude of the potential difference across lightbulbs a, b, c, d, and e from largest to smallest.
if any light bulbs have the same potential difference across them, set them equal. so for example if all bulbs had the same potential difference you would set each to a value of 1.
this means you might not use all 3 numbers.

Explanation:

(First Question):

Step1: Recall Ohm's Law

Ohm's Law states $V = IR$, which rearranges to $I = \frac{1}{R}V$.

Step2: Relate slope to resistance

In the $I$ vs $V$ graph, slope $m = \frac{1}{R}$, so $R = \frac{1}{m}$. A smaller slope means larger $R$.

Step3: Evaluate all options

• Option1: Matches $R = \frac{1}{m}$ (small slope → large $R$).
• Option2: Graph shows $I$ increases with $V$, not vice versa.
• Option3: Contradicts $R = \frac{1}{m}$.
• Option4: Incorrect; $V$ depends on $I$ and $R$ (Ohm's Law).

(Second Question):

Step1: Define battery voltage

Let battery voltage be $V_{batt}$.

Step2: Find voltage for Bulb A

Circuit1: Bulb A is alone, so $V_A = V_{batt}$.

Step3: Find voltage for Bulbs B,C

Circuit2: Bulbs B,C are in series. Identical bulbs split voltage: $V_B = V_C = \frac{V_{batt}}{2}$.

Step4: Find voltage for Bulbs D,E

Circuit3: Bulbs D,E are in parallel. Parallel bulbs have full battery voltage: $V_D = V_E = V_{batt}$.

Step5: Rank voltages

Compare values: $V_A = V_D = V_E > V_B = V_C$.

Answer:

(First Question):
The smaller the slope of the line the greater the resistance.

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