Q. A torch bulb rated as $4.5\, W , 1.5 \, V$ is connected as shown in fig. the e.m.f. of the cell, needed to make the bulb glow at full intensity is :

Current Electricity Report Error

A

$4.5\, V$

B

$1.5 \, V$

C

$2.67 \, V$

D

$13.5 V$

Solution:

Resistance of bulb is given as
$R_{b}=\frac{(1.5)^{2}}{4.5}=0.5 \, \Omega$
The equivalent of $0.5 \,\Omega$ and $1\, \Omega$ in parallel combination which is connected across the battery is given as
$R=\frac{0.5 \times 1}{0.5+1}=0.33 \,\Omega$
Current drawn from battery is given as
$i=\frac{E}{2.67+0.33}=\frac{E}{3}$
Current through the bulb is
$i_{ b }=\frac{E}{3} \times \frac{1}{1+0.5}=\frac{2 E}{9}$
For correct power dissipation in the bulb we use
$\left(\frac{2 E}{9}\right)^{2} \times 0.5=4.5$
$\Rightarrow E =13.5 \,V$

Questions from Current Electricity

1. Two sources of equal emf are connected to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2 (R_2 > R_1).$ If the potential difference across the source having internal resistance $R_2$, is zero, then :

AIEEE 2005

2. In the network shown in figure, each resistance is equal to $2 \Omega$. The resistance between the points $A$ and $B$ is

3. A letter ' $A$ ' is constructed from a uniform wire with resistance $1.0\, \Omega$ per $cm .$ The sides of the letter are $20\, cm$ and the cross piece in the middle is $10\, cm$ long. The apex angle is $60^{\circ} .$ The resistance between the ends of the legs is

4. The diagrams show five different ways in which currents $i_{1}, i_{2}, i_{3}$ can combine at a junction.

For which of these junctions, is the following equation correct ?
$i_{1}+i_{2}=i_{3}+i_{4}$

5. A battery of emf, $10\, V$ is connected to resistances as shown in figure. The potential difference $V_{A}-V_{B}$ between the points $A$ and $B$ is

Physics Most Viewed Questions

1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

NEET 2021 Physical World, Units and Measurements

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

NEET 2020 Dual Nature of Radiation and Matter

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

NEET 2021 Motion in a Straight Line

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

NEET 2020 Electromagnetic Induction

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

NEET 2020 Mechanical Properties of Fluids