Question

A 100 ohm and a 50-ohm resistor are wired to a 12 V battery as shown in the diagram below. From the list of statements listed below please select the correct statements

(A) The resistors are wired in parallel
(B) The resistors are wired in series
(C) The potential difference across these resistors is the same
(D) The potential difference across the 100 resistor is higher
(E) The electrical current passing through 50 resistor is half the current through 100 resistor

Answer 1

If you remove either of the resistors, the other resistor will form a complete circuit with the 12V battery.

Complete step by step answer:
In this question there is a circuit which contains 2 resistors, a 100-ohm resistor and a 50-ohm resistor along with a 12 Volt battery connected as shown in the diagram. Since this is a multiple-choice correct question, we must test each option accordingly.
(A) TRUE because in a parallel connection, each resistor has an equal potential difference across it. Since both the resistors here have been connected to do the 12 Volt battery individually, which means if you remove either of the resistors, the other will form a complete circuit with the battery.
(B) FALSE because in series, both the resistors will have different potential differences if they have different resistances which is not true because both the resistors have same potential difference of 12 Volt across them.
(C) TRUE because that is the reason why both the resistors are in parallel connection. If you remove either of the resistors the other forms a complete circuit with the 12 Volt cell.
(D)FALSE because in the previous option we saw both the resistors have equal potential across them that is 12 Volt.
(E) FALSE because if we calculate the current across both the resistors, we know by ohms law
$V = IR$
$\therefore I = \dfrac{V}{R}$
So current across 100-ohm resistor will be
$I = \dfrac{{12}}{{100}} = 0.12A$
and current across 50-ohm resistor will be
$I = \dfrac{{12}}{{50}} = 0.24A$

Note: The calculations here are done since the battery doesn't have any internal resistance. If the internal resistance is taken into consideration, then the values of current and potential might change.