Answer :
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:
[tex]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}}[/tex]
- Simplifying common terms, we have:
[tex]\frac{1}{Req} = \frac{1}{R_{1}} +\frac{1}{R_{2} } +\frac{1}{R_{3}}[/tex]
- 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).
The correct option is option (C)
All choices listed are definitely true.
Parallel combination of resistances:
(a) As the resistors are connected in parallel, the voltage drop across all the resistors will be the same, since they are connected in a parallel connection across the terminals of the battery, the voltage drop will be equal to battery voltage.
(b) Let us consider that all the resistances have a resistance equal to R
So, the equivalent resistance is given by:
[tex]\frac{1}{R_{eq}}= \frac{1}{R}+ \frac{1}{R}+ \frac{1}{R}\\\\ \frac{1}{R_{eq}}= \frac{3}{R}\\\\R_{eq}= \frac{R}{3}[/tex]
So, we can see that equivalent resistance is less than each resistance in a parallel combination
(d) According to the charge conservation principle, the sum of the currents passing through these resistors is equal to the current passing through the battery (Kirchoff's Current Law).
Learn more about Kirchoff's Current Law:
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