Question:

A circuit is made using $R_1, R_2, R_3, R_4$ and a battery as shown in the following figure. Find the equivalent resistance of the given circuit and the current passing through $R_3$

Updated On: Apr 2, 2024
  • $3 \Omega , \frac{1}{3} A$
  • $\frac{1}{3} \Omega , 27 A $
  • $\frac{2}{3} \Omega , \frac{21}{2} A $
  • $\frac{1}{3} \Omega , \frac{21}{2} A $
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The Correct Option is B

Solution and Explanation

The circuit can be redrawn as shown in the figure below,



So, the equivalent resistance of the three parallel branches is given as,
$R_{e q}=\frac{1}{\frac{1}{0.5+0.5}+\frac{1}{1}+\frac{1}{1}}=\frac{1}{3} \Omega$
Now, from Ohm's law
$I=\frac{V}{R}=\frac{27}{1 / 3}=27 \times 3=18\, A$
Here in the figure, 3 branches are of equal resistance, so current will divide equally in each branch, So, current in $R_{3}$,
$I_{R_{3}}=\frac{27 \times 3}{3}=\frac{81}{3}=27\, A$
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Concepts Used:

Current Electricity

Current electricity is defined as the flow of electrons from one section of the circuit to another.

Types of Current Electricity

There are two types of current electricity as follows:

Direct Current

The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.

Alternating Current

The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.