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What is the magnitude of the current in the resistor? (V1=7.8 V, V2=9.3 V, R=33 Ω.)


To find the current in the resistor \( R \), we first need to calculate the net voltage across the circuit. In the given circuit, we have two voltage sources: \( V_1 \) and \( V_2 \). The polarity of the batteries suggests that they are connected in opposition to each other. Therefore, the net voltage \( V_{\text{net}} \) is the difference between \( V_2 \) and \( V_1 \):

\[
V_{\text{net}} = V_2 - V_1
\]

Given:
- \( V_1 = 7.8 \, \text{V} \)
- \( V_2 = 9.3 \, \text{V} \)
- \( R = 33 \, \Omega \)

Now, we can calculate the current \( I \) using Ohm's law:

\[
I = \frac{V_{\text{net}}}{R}
\]

Let me calculate the value for you.The magnitude of the current through the resistor is approximately \( 0.0455 \, \text{A} \) or 45.5 mA.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:
1. What happens if the values of \( V_1 \) and \( V_2 \) are switched?
2. How would the current change if the resistance \( R \) were doubled?
3. How does the direction of current change when \( V_1 \) becomes greater than \( V_2 \)?
4. What is the power dissipated by the resistor in this circuit?
5. How would adding another resistor in series affect the current?

**Tip**: In circuits with opposing voltage sources, always subtract the smaller voltage from the larger one to find the net voltage.

What is the magnitude of the current in the resistor? (V1=7.8 V, V2=9.3 V, R=33 Ω.)

Find out how to calculate the current in a resistor when two opposing voltage sources (V1=7.8 V and V2=9.3 V) are applied. Use Ohm's Law and key concepts in electric circuits to solve this problem. Suitable for high school students.

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