
The amount of charge Q passed in time t through a cross-section of a wire is $Q = 5{t^2} + 3t + 1$. The value of current at time t=5 s is
A) 9 A
B) 49 A
C) 53 A
D) None of these
Answer
162k+ views
Hint:This question is from electricity. The problem is solved by the Electric Current concept. Apply the Electric Current equation to find the current (I) at the given time (t)
Formula Used:
$I = \dfrac{{dQ}}{{dt}}$
Where,
I = Current
Q = Charge
t = time
Complete answer:
The differential limit gives the current at any instant if the rate of charge flow is not constant:
$I = \dfrac{{dQ}}{{dt}}$
\[I = \dfrac{{d(5{t^2} + 3t + 1)}}{{dt}}\]
\[I = 10t + 3\]
\[I = 10 \times 5 + 3 = 53\]A
Hence, the correct option is Option C) 53 A.
Additional Information:
i) The electric current is a flow of charged particles (electrons) through wires and other components.
ii) Electric current is the rate of flow of charge.
iii) Electric current flows from the negative terminal of the cell to the positive terminal.
iv) The conventional direction of electric current is taken as opposite to the direction of the flow of charge (electrons).
Note: The S.I unit of charge is coulomb and the S.I unit of electric current is ampere (coulomb per second). Pay attention to the units while putting all the values in the questions.
Formula Used:
$I = \dfrac{{dQ}}{{dt}}$
Where,
I = Current
Q = Charge
t = time
Complete answer:
The differential limit gives the current at any instant if the rate of charge flow is not constant:
$I = \dfrac{{dQ}}{{dt}}$
\[I = \dfrac{{d(5{t^2} + 3t + 1)}}{{dt}}\]
\[I = 10t + 3\]
\[I = 10 \times 5 + 3 = 53\]A
Hence, the correct option is Option C) 53 A.
Additional Information:
i) The electric current is a flow of charged particles (electrons) through wires and other components.
ii) Electric current is the rate of flow of charge.
iii) Electric current flows from the negative terminal of the cell to the positive terminal.
iv) The conventional direction of electric current is taken as opposite to the direction of the flow of charge (electrons).
Note: The S.I unit of charge is coulomb and the S.I unit of electric current is ampere (coulomb per second). Pay attention to the units while putting all the values in the questions.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Young's Double Slit Experiment Step by Step Derivation

JEE Electricity and Magnetism Important Concepts and Tips for 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

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

Wheatstone Bridge for JEE Main Physics 2025

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

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

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Uniform Acceleration

Degree of Dissociation and Its Formula With Solved Example for JEE
