Figure shows three resistor configurations $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ connected to $3 \mathrm{~V}$ battery. If the power dissipated by the configuration $\mathrm{R} 1, \mathrm{R} 2$ and $\mathrm{R} 3$ is $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$, respectively, then
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At room temperature, copper has free electron density of $8.4 \times {10^{28}}$ per ${m^3}$. The copper conductor has a cross-section of $10^{-6} \,m^2$ and carries a current of $5.4\, A$. The electron drift velocity in copper is
The current in a simple series circuit is $5.0\, amp$. When an additional resistance of $2.0\, ohms$ is inserted, the current drops to $4.0\, amp$. The original resistance of the circuit in $ohms$ was
A wire of resistor $R$ is bent into a circular ring of radius $r$. Equivalent resistance between two points $X$ and $Y$ on its circumference, when angle $XOY$ is $\alpha$, can be given by
Resistances ${R_1}$ and ${R_2}$ are joined in parallel and a current is passed so that the amount of heat liberated is ${H_1}$ and ${H_2}$ respectively. The ratio $\frac{{{H_1}}}{{{H_2}}}$ has the value
Two resistors are joined in parallel whose, resultant is $\frac{6}{5} \,\Omega$. One of the resistance wire is broken and the effective resistance becomes $2 \,ohms$. Then the resistance (in $ohm$) of the wire that got broken is ..........