Potential Difference in a Circuit Loop
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In Fig. 27-26, the ideal batteries have emfs $\mathcal{E}_1 = 150\text{ V}$ and $\mathcal{E}_2 = 50\text{ V}$ and the resistances are $R_1 = 3.0\text{ }\Omega$ and $R_2 = 2.0\text{ }\Omega$. If the potential at $P$ is $100\text{ V}$, what is it at $Q$?
This question includes visual content: The image displays a circuit schematic featuring a rectangular loop. On the left branch, there is a battery with EMF $\mathcal{E}_1$ oriented with the negative terminal above and positive below. On the right branch, there is a battery with EMF $\mathcal{E}_2$ with the negative terminal above and positive below. The top horizontal branch contains a resistor $R_1$, and the bottom horizontal branch contains a resistor $R_2$. Point $Q$ is marked at the top-left corner above battery $\mathcal{E}_1$. Point $P$ is marked at the bottom-right corner below battery $\mathcal{E}_2$.
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Step by Step Written Solution
Hi Dinara, let's solve this circuit problem to find the electric potential at point Q.
Circuit Parameters
First, let's redraw the circuit to clearly show the polarities and nodes. Notice that both batteries have their negative terminals at the top.
To find the potential at Q, we first need to find the current flowing in the single loop. We will use Kirchhoff's loop rule, summing potential changes clockwise.
Step 1: Find the Current I
Assume the current flows clockwise. Starting from point Q and going around the loop, we have potential drops across resistors and changes across batteries.
Let's substitute the given values: negative three times I, plus fifty, minus two times I, minus one hundred fifty, equals zero.
Simplifying the equation, we get negative five times I minus one hundred equals zero.
Solving for I, we find it is negative twenty Amperes. This means the current actually flows counter-clockwise with a magnitude of twenty Amperes.
Now that we have the current, we can find the potential at point Q by starting from point P, where the potential is one hundred volts.
Step 2: Calculate Potential at Q
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