The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as $R_1$ has the colour code (Orange, Red, Brown). The resistors $R_2$ and $R_4$ are $80\, \Omega $ and $40\,\Omega $, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $R_3$ would be
$\therefore $ Colour code of $\mathrm{R}_{3}$ be Brown, Blue, Brown.
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With a potentiometer null point were obtained at $140\, cm$ and $180\, cm$ with cells of $emf$ $1.1 \,V$ and one unknown $X\, volts$. Unknown $emf$ is .............. $V$
A letter $'A'$ is constructed of 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 $60$ . The resistance between the ends of the legs is close to ................ $\Omega$
A $10\,V$ battery with internal resistance $1\,\Omega $ and a $15\,V$ battery with internal resistance $0.6\,\Omega $ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to ................ $V$
Four wires $AB,\,\,BC,\,\,CD,\,\,DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$ of which $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is
To get maximum current through a resistance of $2.5\,\Omega $, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega $. What are the values of $n$ and $m$ if the total number of cells is $45$ ?
In a meter bridge, the wire of length $1\, m$ has a nonuniform cross-section such that, the variation $\frac{{dR}}{{d\ell }}$ of its resistance $R$ with length $\ell $ is $\frac{{dR}}{{d\ell }} \propto \frac{1}{{\sqrt \ell }}$ Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point $P$. What is the length $AP$ ? ................ $m$
The current density in a cylindrical wire of radius $r=4.0 \,mm$ is $1.0 \times 10^{6} \,A / m ^{2}$. The current through the outer portion of the wire between radial distances $r / 2$ and $r$ is $x \pi A$; where $x$ is ..........
The charge flowing through a resistance $R$ varies with time $t$ as $ Q=at-bt^2 $ where $a$ and $b$ are positive constants . The total heat produced in $R$ is