Question

Consider three different resistors connected to a battery in parallel.

Answer 1

Answer:

c) All choices listed are definitely true.

Explanation:

a)

• As they are connected in parallel, the voltage drop is equal in all the resistors, by definition of a parallel connection, and equal to the terminal voltage of the battery (assuming that the internal resistance of the battery is negligible).

b)

• Applying Ohm's law to the circuit, we arrive to the following expression:

        $I_{tot} = I_{1} +I_{2} + I_{3} \\ I_{tot} =\frac{V}{Req} = \frac{V}{R_{1}} +\frac{V}{R_{2} } +\frac{V}{R_{3}}$

• Simplifying common terms, we have:

       $\frac{1}{Req} = \frac{1}{R_{1}} +\frac{1}{R_{2} } +\frac{1}{R_{3}}$

• It can be seen that the equivalent resistance, is less than any of the resistances.

d)

• Due to the charge conservation principle, as the current is made from moving charges, the sum of the currents passing through these resistors is equal to the current passing through the battery (KCL).