Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
General Ability
Chapter
General Science

NDA 2024 · General Ability · General Science

An electrical circuit is given below. V_1=1 V and Resistance R=1000...

An electrical circuit is given below. V1=1V\mathrm{V}_1=1 \mathrm{ V} and Resistance R=1000Ω\mathrm{R}=1000 \Omega.
The current through the resistance RR is very close to 1 mA and the voltage across point A and B , VAB=1V\mathrm{V}_{\mathrm{AB}}=1 \mathrm{ V}. Now the circuit is changed to:
where value of V2=5V\mathrm{V}_2=5 \mathrm{ V}. The internal resistances of both the batteries are 0.1Ω0.1 \Omega. The current through the resistance R is about:

Options

  1. A1.0 mA
  2. B1.2 mA
  3. C3.0 mA
  4. D5.0 mA

Correct answer

C. 3.0 mA

Step-by-step solution

\begin{aligned} & \text{Equivalent voltage }=\frac{\varepsilon_1 r_1+\varepsilon_2 r_2}{r_1+r_2} \\ & \qquad \begin{aligned} & =\frac{1 \times 0.1+5 \times 0.1}{0.1+0.1} \\ \mathrm{E}_{\mathrm{eq}} & =\frac{0.6}{0.2}=3 \mathrm{ V} \end{aligned} \end{aligned}Fromfirstcircuit,wehaveFrom first circuit, we havei=\frac{\varepsilon}{\mathrm{R}+r}ValueofValue ofrisverylesscanbeneglectedascomparedtoRNow,is very less can be neglected as compared to R Now,i=εR10−3=1RR=103=1000Ω\begin{aligned} i & =\frac{\varepsilon}{\mathrm{R}} \\ 10^{-3} & =\frac{1}{\mathrm{R}} \\ \mathrm{R} & =10^3=1000 \Omega \end{aligned}Now,fromsecondcircuitNow, from second circuiti1=EeqR+req=31000i1=3×10−3=3mA\begin{aligned} i_1 & =\frac{\mathrm{E}_{\mathrm{eq}}}{\mathrm{R}+r_{e q}}=\frac{3}{1000} \\ i_1 & =3 \times 10^{-3} \\ & =3 \mathrm{ mA} \end{aligned}$
Practice General Science on Quantrex Academy →

More from General Science

For an object in gravitational field, the gravitational potential is the same at two… NDA 2026A very large container consists of an ideal gas. The speed of sound in the gas is x .… NDA 2026A constant power machine pulls a block on a smooth horizontal surface. Which one of the… NDA 2026A ball is dropped from rest from height h above the ground in frame S (the Earth's… NDA 2026A pendulum of length L oscillates with an angular amplitude of θ = 60^ ^ ∘ and time… NDA 2026A solid of mass m has temperature-dependent specific heat as C(T) = C_0 + α T , where C_0… NDA 2026In a certain process, the relation between pressure (P) and volume (V) , for an ideal… NDA 2026An object is placed far beyond the centre of curvature of a concave mirror. The object… NDA 2026 Full General Science list All NDA PYQs