A milliammeter of range $10\, mA$ and resistance $9\, \Omega$ is joined in a circuit as shown. The meter gives full-scale deflection for current $I$ when $A$ and $B$ are used as its terminals, i.e., current enters at $A$ and leaves at $B$ ($C$ is left isolated). The value of $I$ is
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A uniform metallic wire of length $L$ is mounted in two configurations. In configuration $1$ (triangle), it is an equilateral triangle and a voltage $V$ is applied to corners $A$ and $B$. In configuration $2$ (circle), it is bent in the form of a circle and the potential $V$ is applied at diametrically opposite points $P$ and $Q$. The ratio of the power dissipated in configuration $1$ to configuration $2$ is
A potentiometer circuit is set up as shown. The potential gradient, across the potentiometer wire, is $k$ $volt/cm$ and the ammeter, present in the circuit, reads $1.0\,\, A$ when two way key is switched off. The balance points, when the key between the terminals $(i)$ $1$ and $2$ $(ii)$ $1$ and $3,$ is plugged in, are found to be at lengths $l_1$ and $l_2$ respectively. The magnitudes, of the resistors $R$ and $X,$ in $ohms$, are then, equal, respectively, to
A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.
An electron (charge $= 1.6 × 10^{-19}$ coulomb) is moving in a circle of radius $5.1 × 10^{-11}\,m$ at a frequency of $6.8 × 10^{15} $ revolutions/sec. The equivalent current is approximately
A current of $10 \,A$ is maintained in a conductor of cross-section $1 \,cm ^2$. If the number density of free electrons be $9 \times 10^{28} \,m ^{-3}$, the drift velocity of free electrons is .......... $m / s$