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Two resistors of 4 Ω and 6 Ω are connected in parallel. The combination is connected across a 6 V battery of negligible resistance. Calculate the current through the battery.

Answer :

Final answer:

The current through the battery can be calculated using Ohm's Law in a parallel circuit. By applying Ohm's Law to each resistor individually and summing the currents, we can find the total current through the battery.

Explanation:

The current through the battery can be calculated using Ohm's Law. In a parallel circuit, the voltage is the same across each resistor. Applying Ohm's Law, we can calculate the current through each resistor separately. The total current through the battery is the sum of the currents through the individual resistors.

Given that the resistors are connected in parallel, we can use the formula:

  • 1/Rtotal = 1/R1 + 1/R2

Substituting the values, we have 1/Rtotal = 1/4 + 1/6 = 5/12. Taking the reciprocal of both sides, we find that Rtotal = 12/5 Ω.

Now, we can use Ohm's Law to calculate the current through each resistor:

  • I1 = V/R1 = 6/4 = 1.5 A
  • I2 = V/R2 = 6/6 = 1 A

The total current through the battery is the sum of the currents through the individual resistors:

  • Itotal = I1 + I2 = 1.5 A + 1 A = 2.5 A

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