In the given circuit the internal resistance of the $18\,V$ cell is negligible. If $R_1 = 400 \,\Omega ,\,R_3 = 100\,\Omega $ and $R_4 = 500\,\Omega $ and the reading of an ideal voltmeter across $R_4$ is $5\,V,$ then the value of $R_2$ will be ........... $\Omega$
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For the circuit shown, with ${R_1} = 1.0\,\Omega $, ${R_2} = 2.0\,\Omega $, ${E_1} = 2\,V$ and ${E_2} = {E_3} = 4\,V$, the potential difference between the points $‘a’$ and $‘b’$ is approximately (in $V$)
A copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance
Resistance of one carbon filament and one tungsten lamp are measured individually when the lamp are lit and compared with their respective resistances when cold. Which one of the following statements will be true
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
Model a torch battery of length $l$ to be made up of a thin cylindrical bar of radius $'a'$ and a concentric thin cylindrical shell of radius ' $b$ ' fille in between with an electrolyte of resistivity $\rho$ (see figure). If the battery is connected to a resistance of value $R ,$ the maximum Joule heating in $R$ will take place for
Two batteries of $e.m.f.$ $4\,V$ and $8 \,V$ with internal resistances $1\, \Omega$ and $2\,\Omega$ are connected in a circuit with a resistance of $9 \,\Omega$ as shown in figure. The current and potential difference between the points $P$ and $Q$ are
.............. $A$ the current flowing through the resistance $R_2$ of the circuit shown in fig if the resistance are equal to $R_1 = 20\ \Omega, R_2 = 30 \ \Omega$ and $R_3 = 60 \ \Omega$ and potentials of points $1, 2$ and $3$ are equal to $V_1= 20\, V,$ $V_2 = 30\ V$ and $V_3 = 60\ V$