Question

The current in the $1\Omega $ resistor shown in the circuit is

A) $\dfrac{2}{3}A$
B) $3A$
C) $6A$
D) $2A$

Answer 1

Hint:The problem is from the electricity part of physics. We can apply the concept of parallel combination and series combination of resistance here. Use the equation for effective resistance in parallel and series combinations.


Formula Used:
Equivalent resistance for a series resistance circuit:
${R_E} = {R_1} + {R_2} + {R_3}$
Equivalent resistance for a parallel resistance circuit:
$\dfrac{1}{{{R_E}}} = \dfrac{1}{{{R_1}}} + \dfrac{1}{{{R_2}}} + \dfrac{1}{{{R_3}}}$
Where ${R_E}$= equivalent resistance and ${R_1},{R_2},{R_3}$ = component resistance.
Ohm’s law:
$V = IR$
Where V = voltage, I = current and R = resistance.


Complete answer:
The equivalent resistance is a single resistance which can replace all the component resistances in a circuit in such a manner that the current in the circuit remains unchanged.
The two $4\Omega $ resistors are in parallel connection. Their equivalent resistance will be
${R_E} = \dfrac{{4 \times 4}}{{4 + 4}} = \dfrac{{16}}{8} = 2\Omega $
Then total resistance of the circuit is
$R = 2 + 1 = 3\Omega $
Current (I) through $1\Omega $resistance
$I = \dfrac{V}{R} = \dfrac{6}{3} = 2A$

Hence, the correct option is Option (D).

Additional Information:
Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance blocks the flow of current. The S.I unit of resistance is ohms. The current decreases as resistance increases. On the other hand, the current increases as the resistance decreases.
When electrons move through a conductor, like a metal wire, an electric current occurs. The ions in the metal can collide with the traveling electrons. Resistance is created as a result and makes it more difficult for the current to flow.


Note: Resistance is a measure of the opposition to current flow in an electrical circuit. Resistance blocks the flow of current. The current decreases as resistance increases. On the other hand, the current increases as the resistance decreases. In short circuit conditions the current through the circuit increases exponentially because resistance of the circuit becomes zero.