In the given circuit,the 5, Omega resistor di | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The circuit consists of a $12\, \Omega$ resistor in series with a parallel combination of two branches. The first branch has a resistance of $9\,

Vedclass · Accepted Answer

$192$

Vedclass · Answer

(B) The circuit consists of a $12\, \Omega$ resistor in series with a parallel combination of two branches. The first branch has a resistance of $9\, \Omega + 6\, \Omega = 15\, \Omega$ and the second branch has a resistance of $5\, \Omega$.Let $i_1$ be the current through the $5\, \Omega$ resistor and $i_2$ be the current through the $15\, \Omega$ branch. Since they are in parallel,the potential difference across them is the same: $i_1 	imes 5 = i_2 	imes 15 \implies \frac{i_1}{i_2} = \frac{15}{5} = 3 \implies i_1 = 3i_2$.The power dissipated in the $5\, \Omega$ resistor is $P_5 = i_1^2 	imes 5 = 45\, W$.$i_1^2 = \frac{45}{5} = 9 \implies i_1 = 3\, A$.Since $i_1 = 3i_2$,we have $3 = 3i_2 \implies i_2 = 1\, A$.The total current $i$ flowing through the $12\, \Omega$ resistor is $i = i_1 + i_2 = 3\, A + 1\, A = 4\, A$.The power dissipated in the $12\, \Omega$ resistor is $P_{12} = i^2 	imes 12 = (4)^2 	imes 12 = 16 	imes 12 = 192\, W$.

In the given circuit,the $5\, \Omega$ resistor dissipates $45\, J/s$ of heat due to the current flowing through it. The power dissipated per second in the $12\, \Omega$ resistor will be .............. $W$.

Similar Questions

The potential difference between the points $P$ and $Q$ is nearly: (in $\,V$)

What should be the relationship between the values of the three resistors shown in the figure so that they produce equal heat energy?

In the given circuit,the current flowing between points $A$ and $B$ and through the battery $E_2$ is:

In the given figure, the current through the $4 \, \Omega$ resistor is ................. $A$.

If the resistance of each edge of a cube-shaped wire frame as shown in the figure below is $R$,then the resistance between points $1$ and $7$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module