High School

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In the given circuit, the ammeter and voltmeter are ideal, and the battery of 6 V has an internal resistance. What are the readings of the voltmeter and ammeter?

Answer :

To determine the battery's emf and internal resistance, one must solve two equations derived from Ohm's law with given currents and resistances. After finding these values, the voltmeter reading will show the voltage across the resistor, and the ammeter will measure the circuit's total current.

To find the electromotive force (emf) and internal resistance of a battery, we can use Ohm's law (V=IR) and the provided data from two different resistances with their corresponding currents.

First, we set up two equations based on the provided information:

  1. For R1 = 10
    Ohm and I1 = 2.0 A, the equation is emf = I1 * (R1 + r).
  2. For R2 = 5
    Ohm and I2 = 3.8 A, the equation is emf = I2 * (R2 + r).

Solving these two equations simultaneously will give us the emf and the internal resistance:

  1. emf = 2.0 A * (10
    Ohm + r)
  2. emf = 3.8 A * (5
    Ohm + r)

We can equate the two expressions:

2.0 A * (10 + r) = 3.8 A * (5 + r)

By simplifying this equation, we can solve for r and then substitute it back into one of the first equations to find the emf. This process will provide the values of internal resistance and emf for the battery.

The voltmeter and ammeter readings can then be determined using Ohm's law once we know these values. The voltmeter will read the potential difference across the resistor, which is the battery's emf minus the voltage drop across the internal resistance. The ammeter will display the current flowing through the circuit, which is determined by the total resistance in the circuit (external resistance plus internal resistance).

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