
The figure shows a circuit that contains four identical resistors with resistance R = 2.0 Ω. Two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9.V. The current ‘i’ just after the switch ‘s’ is closed will be

A. 9A
B. 3.0 A
C. 2.25 A
D. 3.37 A
Answer
162.6k+ views
Hint: At the instant when the switch is closed, it is derived from basic concepts that the inductor behaves like a resistance of infinite value. Based on the above inference the circuit can be redrawn to analyse its behavior just as the switch is closed.
Formula used:
Basic form of Ohm’s Law assuming ideal conditions is written below
\[V = I \times R\] ………… (1)
Where, V= Voltage across a resistive element in Volts
I= Current through the resistive element in Amperes
R= Resistance offered to the flow of current by the element in Ohms
Complete answer:
Here, after redrawing the circuit to represent the state just after the switch is closed. The inductor is assumed to be a resistance of infinite value.
Image: Circuit just after switch is closed
Data given:
R= 2.0 ohm
L= 2mH (milli Henry)
E=9 V
Putting the values given above and using Ohm’s Law (1) for the circuit drawn above (2), we can write ,
\[\dfrac{V}{I} = R\]
\[R = \]\[2 + 2 = 4\] Ohm
Here, The equivalent resistance is added because the resistances given are in series.
\[I = \dfrac{V}{R} = \dfrac{9}{4} = 2.25\] Amperes
Hence, the current just after the switch is closed is 2.25 Amperes.
The correct answer is C.
Note: This problem deals with transient state analysis. During the transient state there is a change in the variables or process, but this stage is temporary and finally the system reaches a steady state. As the circuit is in a transient state just after the switch is closed, the inductor behaves as open circuit. Students often make a common mistake to solve the given question. They used a second loop to solve. Here we need to use the first loop.
Formula used:
Basic form of Ohm’s Law assuming ideal conditions is written below
\[V = I \times R\] ………… (1)
Where, V= Voltage across a resistive element in Volts
I= Current through the resistive element in Amperes
R= Resistance offered to the flow of current by the element in Ohms
Complete answer:
Here, after redrawing the circuit to represent the state just after the switch is closed. The inductor is assumed to be a resistance of infinite value.

Image: Circuit just after switch is closed
Data given:
R= 2.0 ohm
L= 2mH (milli Henry)
E=9 V
Putting the values given above and using Ohm’s Law (1) for the circuit drawn above (2), we can write ,
\[\dfrac{V}{I} = R\]
\[R = \]\[2 + 2 = 4\] Ohm
Here, The equivalent resistance is added because the resistances given are in series.
\[I = \dfrac{V}{R} = \dfrac{9}{4} = 2.25\] Amperes
Hence, the current just after the switch is closed is 2.25 Amperes.
The correct answer is C.
Note: This problem deals with transient state analysis. During the transient state there is a change in the variables or process, but this stage is temporary and finally the system reaches a steady state. As the circuit is in a transient state just after the switch is closed, the inductor behaves as open circuit. Students often make a common mistake to solve the given question. They used a second loop to solve. Here we need to use the first loop.
Recently Updated Pages
JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Charging and Discharging of Capacitor

Wheatstone Bridge for JEE Main Physics 2025

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

In which of the following forms the energy is stored class 12 physics JEE_Main
