Answer
Verified
91.2k+ views
Hint: The question can be solved by grounding one end of the wire and then applying Kirchhoff’s Current Law to the loop formed. Kirchhoff’s Voltage Law can also be used to solve this problem.
Complete Step by Step Solution: Kirchhoff’s Current Law, deals with the conservation of charge entering and leaving a junction. Kirchhoff’s Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.”
This law is used to describe how a charge enters and leaves a wire junction point or node on a wire.
Connect the lower wire of the $1\Omega $ resistor to the ground (Q end) and apply KCL. Consider the grounded circuit as shown below.
Applying, KCL at the Q point, we can write,
$\dfrac{{V + 6}}{3} + \dfrac{V}{1} = \dfrac{{9 - V}}{5}$
$ \Rightarrow V\left[ {\dfrac{1}{3} + \dfrac{1}{5} + 1} \right] = \dfrac{9}{5} - 2$
Simplifying the equation further,
$ \Rightarrow V\left[ {\dfrac{{5 + 3 + 15}}{{15}}} \right] = \dfrac{{9 - 10}}{5}$
The potential difference between points Q and P is given by,
$ \Rightarrow V = - \dfrac{1}{5} \times \dfrac{{15}}{{23}} = \dfrac{{ - 3}}{{23}} = - 0.13V$
Thus the current in the 1Ω resistor is ${\text{I = }}\dfrac{{\text{V}}}{{\text{R}}}{\text{ = }}\dfrac{{{\text{0}}{\text{.13}}}}{{\text{1}}}{\text{ = 0}}{\text{.13A}}$.
The current flows from Q to P. The correct answer is Option C.
Note: Kirchhoff's voltage law (KVL) states that the sum of all voltages around any closed loop in a circuit must be equal to zero. This is a consequence of charge conservation and also conservation of energy. This means that the sum of all potential differences across the component involved in the circuit gives a zero reading, as expected.
Assuming potential at Q is $V$, we apply KVL loop 1,
$9 - 2i - 1\left( {i - {i_1}} \right) - 3i = 0$.
When we apply KVL to loop 2,
$6 - 3{i_1} + 1\left( {i - {i_1}} \right) = 0$.
Solving the equations for the two loops,
${\text{i = 1}}{\text{.82A}}$ and ${{\text{i}}_{\text{1}}}{\text{ = 1}}{\text{.95A}}$.
Current through the $1\Omega $ resistor is ${\text{0}}{\text{.13A}}$.
Complete Step by Step Solution: Kirchhoff’s Current Law, deals with the conservation of charge entering and leaving a junction. Kirchhoff’s Current Law, often shortened to KCL, states that “The algebraic sum of all currents entering and exiting a node must equal zero.”
This law is used to describe how a charge enters and leaves a wire junction point or node on a wire.
Connect the lower wire of the $1\Omega $ resistor to the ground (Q end) and apply KCL. Consider the grounded circuit as shown below.
Applying, KCL at the Q point, we can write,
$\dfrac{{V + 6}}{3} + \dfrac{V}{1} = \dfrac{{9 - V}}{5}$
$ \Rightarrow V\left[ {\dfrac{1}{3} + \dfrac{1}{5} + 1} \right] = \dfrac{9}{5} - 2$
Simplifying the equation further,
$ \Rightarrow V\left[ {\dfrac{{5 + 3 + 15}}{{15}}} \right] = \dfrac{{9 - 10}}{5}$
The potential difference between points Q and P is given by,
$ \Rightarrow V = - \dfrac{1}{5} \times \dfrac{{15}}{{23}} = \dfrac{{ - 3}}{{23}} = - 0.13V$
Thus the current in the 1Ω resistor is ${\text{I = }}\dfrac{{\text{V}}}{{\text{R}}}{\text{ = }}\dfrac{{{\text{0}}{\text{.13}}}}{{\text{1}}}{\text{ = 0}}{\text{.13A}}$.
The current flows from Q to P. The correct answer is Option C.
Note: Kirchhoff's voltage law (KVL) states that the sum of all voltages around any closed loop in a circuit must be equal to zero. This is a consequence of charge conservation and also conservation of energy. This means that the sum of all potential differences across the component involved in the circuit gives a zero reading, as expected.
Assuming potential at Q is $V$, we apply KVL loop 1,
$9 - 2i - 1\left( {i - {i_1}} \right) - 3i = 0$.
When we apply KVL to loop 2,
$6 - 3{i_1} + 1\left( {i - {i_1}} \right) = 0$.
Solving the equations for the two loops,
${\text{i = 1}}{\text{.82A}}$ and ${{\text{i}}_{\text{1}}}{\text{ = 1}}{\text{.95A}}$.
Current through the $1\Omega $ resistor is ${\text{0}}{\text{.13A}}$.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main