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In a circuit, a nonideal 12 V battery is connected to a single resistor with a resistance of 62 ohms. A voltmeter across the resistor indicates a reading of 9 V. What is the internal resistance of the battery?

a. 2 ohms
b. 3 ohms
c. 4 ohms
d. 6 ohms
e. 14 ohms

Answer :

Final answer:

The internal resistance of the battery can be found by first calculating the current through the circuit using Ohm's law and then determining the voltage drop across the internal resistance, which, after calculations, turns out to be 3 ohms. Therefore the correct option is B

Explanation:

To calculate the internal resistance of the battery, we can use the provided voltage across the resistor and the known values to determine the current in the circuit. Since the voltage across the resistor is 9 V and the resistance is 62 ohms, using Ohm's law (V = IR), the current (I) flowing through the circuit can be found by I = V/R = 9 V / 62 ohms, which gives us the current in amperes (A).

Now that we have the current, we can find the voltage drop (Vdrop) across the internal resistance of the battery. The total voltage of the battery (emf) is 12 V, and the voltage across the resistor is 9 V, so the difference, Vdrop = 12 V - 9 V, is due to the internal resistance.

Now, applying Ohm's law again for the internal resistance (r), we have Vdrop = I * r. We can solve for r = Vdrop / I. With the current already found in the first step and the voltage drop calculated, we can plug in the values to solve for r.

After performing the calculations, it can be seen that the internal resistance is 3 ohms.

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Rewritten by : Barada

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