NDA 1 2024 GAT Q52: An electric circuit is given below. V 1=1 V and Resistance…

NDA 1 2024 GAT, question 52

Topic: Physics

Q52

An electric circuit is given below. $V_{1}=1\text{ V}$ and Resistance $R=1000\ \Omega$ .

Figure for Q52

The current through the resistance $R$ is very close to $1\text{ mA}$ and the voltage across point $A$ and $B$ , $V_{AB}=1\text{ V}$ . Now the circuit is changed to :

Figure for Q52

where value of $V_{2}=5\text{ V}$ . The internal resistances of both the batteries are $0.1\ \Omega$ . The current through the resistance $R$ is about :

(a) $1.0\text{ mA}$
(b) $1.2\text{ mA}$
(c) $3.0\text{ mA}$ Correct answer
(d) $5.0\text{ mA}$

Solution.

Answer: (c) $3.0\text{ mA}$

The two cells have the same polarity and equal internal resistances.
Their parallel equivalent emf is (1 + 5)/2 = 3 V and internal resistance is 0.1/2 = 0.05 Ω.
The load current is 3/1000.05 A ≈ 3.0 mA.
The internal resistances matter: the 5 V cell does not simply set the terminal voltage to 5 V.