Resistance Calculation from Electric Potential Graph
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4. Figure 27-27 shows a circuit of four resistors that are connected to a larger circuit. The graph below the circuit shows the electric potential $V(x)$ as a function of position $x$ along the lower branch of the circuit, through resistor 4; the potential $V_A$ is $12.0\text{ V}$. The graph above the circuit shows the electric potential $V(x)$ versus position $x$ along the upper branch of the circuit, through resistors 1, 2, and 3; the potential differences are $\Delta V_B = 2.00\text{ V}$ and $\Delta V_C = 5.00\text{ V}$. Resistor 3 has a resistance of $200\text{ }\Omega$. What is the resistance of (a) resistor 1 and (b) resistor 2?
This question includes visual content: The image contains two parts. On the left is a circuit diagram with a resistor labeled '4' in a lower parallel branch. Above it is another branch containing three resistors labeled '1', '2', and '3' in series. On the right is a graph of electric potential V versus position x along the upper branch. The graph shows a decreasing potential curve across the three resistors. Specifically, it shows a vertical drop labeled ΔV_B across resistor 2 and another drop labeled ΔV_C across resistor 3, with dashed lines projecting from the resistors onto the x-axis of the graph.
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Hi Dinara, let's solve this electric circuit problem together. First, let's analyze how the circuit is connected.
Analyzing the Circuit
The circuit has two parallel branches. The upper branch consists of three resistors in series, which are resistor one, resistor two, and resistor three. The lower branch contains only resistor four.
• Upper branch: Resistors 1, 2, and 3 in series
• Lower branch: Resistor 4
From the graph of the lower branch, we see that the total potential drop across resistor four is equal to V sub A, which is twelve point zero volts.
Since parallel branches must have the same potential difference, the total potential difference across the upper branch is also twelve point zero volts.
Now let's find the potential drop across each resistor in the upper branch.
Potential Drops in the Upper Branch
For series resistors, the total potential difference is the sum of the individual potential differences across each resistor.
The graph shows that the potential drop across resistor two is delta V sub B, which is two point zero zero volts. The drop across resistor three is delta V sub C, which is five point zero zero volts.
Substituting these values, we can write our potential equation as delta V sub one plus two point zero zero plus five point zero zero equals twelve point zero.
Solving for delta V sub one, we get twelve minus seven, which equals five point zero zero volts.
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