Video Transcript
Consider the circuit below. When changing the value of 𝑅 𝑣,
which of the following graphs represents the relation between 𝑅 𝑣 and the reading
of the ammeter? (A), (B), (C), (D).
In this circuit, we have a cell and
a variable resistor. The cell produces a potential
difference across the variable resistor, and this potential difference produces a
current in the variable resistor. We also see that an ammeter and
voltmeter are connected as parts of the circuit. The ammeter is used to measure the
current in the circuit, and the voltmeter is used to measure the potential
difference across the resistor.
To determine how the current will
change when the resistance is varied, we will need to use Ohm’s law. Recall that Ohm’s law states for
two points in a circuit, the potential difference across the points equals the
current between the points multiplied by the resistance of the object between the
points. Ohm’s law can be written as an
equation, 𝑉 equals 𝐼𝑅, where 𝑉 stands for the potential difference across the
resistor, 𝐼 stands for the current in the resistor, and 𝑅 stands for the
resistance of the resistor.
To find the relationship between
the resistance and the current, we can make 𝑅 the subject of the equation. We can do this by dividing both
sides of the equation by the current. This gives us the equation
resistance 𝑅 is equal to the potential difference divided by the current. Since the potential difference 𝑉
from the cell will remain the same, this means that the resistance 𝑅 is inversely
proportional to the current 𝐼. So, when the resistance of the
variable resistor is increased, the current will decrease.
Now, we can look at the graphs and
determine which of these graphs correctly represents the resistance 𝑅 being
inversely proportional to the current 𝐼. Option (B) shows a quadratic
relation between the current and the resistance. It shows that as the resistance
increases, the current increases, which is incorrect. So, this graph is incorrect. Option (C) shows that the current
remains constant when the resistance is increased, which is incorrect. So, this graph is incorrect.
Option (D) shows a linear relation
between current and resistance. It shows that as the resistance
increases, the current increases, which is also incorrect. So, this graph is incorrect. This leaves option (A). This graph shows the resistance is
inversely proportional to the current.
Therefore, option (A) is the
correct answer. Graph (A) correctly represents the
relation between 𝑅 𝑣 and the reading of the ammeter when the value 𝑅 𝑣 is
changed.
