Question

Two identical batteries each of emf $$2\,V$$  and internal resistance $$1\,\Omega $$  are available to produce heat in an external resistance by passing a current through it. The maximum power that can be developed across $$R$$ using these batteries is

A. $$3.2\,W$$
B. $$2\,W$$  
C. $$1.28\,W$$
D. $$\frac{8}{9}W$$
Answer :   $$2\,W$$
Solution :
To receive maximum current, the two batteries should be connected in series.
Given, $$R = 1\,\Omega + 1\,\Omega = 2\,\Omega .$$
Hence, power developed across the resistance $$R$$ with the batteries in series is
$$\eqalign{ & P = {i^2}R = {\left( {\frac{{2E}}{{R + 2r}}} \right)^2}R\,\,\,\left[ {I = \frac{E}{{{R_{{\text{eq}}}}}}} \right] \cr & = \left( {\frac{{2 \times 2}}{{2 + 2}}} \right) \times 2 = 2\,W\,\,\left[ {\because r = 1\,\Omega } \right] \cr} $$
NOTE
In case of batteries connected in series, equivalent emf is given by $${E_{{\text{eq}}}} = {E_1} + {E_2}$$

Releted MCQ Question on
Electrostatics and Magnetism >> Electric Current

Releted Question 1

The temperature coefficient of resistance of a wire is 0.00125 per $$^ \circ C$$ At $$300\,K,$$  its resistance is $$1\,ohm.$$  This resistance of the wire will be $$2\,ohm$$  at.

A. $$1154\,K$$
B. $$1100\,K$$
C. $$1400\,K$$
D. $$1127\,K$$
Releted Question 2

A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if

A. both the length and the radius of the wire are halved.
B. both the length and the radius of the wire are doubled.
C. the radius of the wire is doubled.
D. the length of the wire is doubled.
Releted Question 3

The electrostatic field due to a point charge depends on the distance $$r$$ as $$\frac{1}{{{r^2}}}.$$ Indicate which of the following quantities shows same dependence on $$r.$$

A. Intensity of light from a point source.
B. Electrostatic potential due to a point charge.
C. Electrostatic potential at a distance r from the centre of a charged metallic sphere. Given $$r$$ < radius of the sphere.
D. None of these
Releted Question 4

The current $$i$$ in the circuit (see Fig) is
Electric Current mcq question image

A. $$\frac{1}{{45}}A$$
B. $$\frac{1}{{15}}A$$
C. $$\frac{1}{{10}}A$$
D. $$\frac{1}{5}A$$

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Electric Current


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