Current Electricity Questions

Alternating current cannot be measured by a D.C. ammeter because:

In an LCR series a.c. circuit, the voltage across each of the components, $L,C$ and $R$ is $50\text{V}$. The voltage across the $LC$ combination will be:

The electrochemical equivalent of a metal is $3.3\times 10^{-7}\text{kg}$ per coulomb. The mass of the metal liberated at the cathode when a $3\text{A}$ current is passed for $2\text{seconds}$ will be:

The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $E=a\theta +b{\theta }^2$ in volts where the ratio $a/b$ is $700^{\circ }\text{C}$. If the cold junction is kept at $0^{\circ }\text{C}$, then the neutral temperature is:

Time taken by a $836\text{W}$ heater to heat one litre of water from $10^{\circ }\text{C}$ to $40^{\circ }\text{C}$ is:

Thermistors are usually made of:

In a metre bridge experiment, a null point is obtained at $20\text{cm}$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X<Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4X$ against $Y$?

An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the length and radii of the wires are in the ratio of $4/3$ and $2/3$, then the ratio of the currents passing through the wires will be:

The resistance of the series combination of two resistances is $S$. When they are joined in parallel, the total resistance is $P$. If $S=nP$, then the minimum possible value of $n$ is:

A $6\text{V}$ battery is connected to a network of resistors. If the equivalent resistance of the network is $1.5\Omega$, the total current supplied by the battery is:

In a LCR circuit, capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to:

The resistance of a wire is $5\Omega$ at $50^{\circ }\text{C}$ and $6\Omega$ at $100^{\circ }\text{C}$. The resistance of the wire at $0^{\circ }\text{C}$ will be:

A material $B$ has twice the specific resistance (resistivity) of $A$. A circular wire made of $B$ has twice the diameter of a wire made of $A$. For the two wires to have the same resistance, the ratio $L_A/L_B$ of their respective lengths must be:

Kirchhoff’s first law ($\sum i=0$) and second law ($\sum iR=\sum E$) are respectively based on the conservation of:

In a Wheatstone’s bridge, three resistances $P,Q$ and $R$ are connected in three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced is:

The current $I$ drawn from the $5\text{V}$ source in the following circuit is:

The resistance of a bulb filament is $100\Omega$ at a temperature of $100^{\circ }\text{C}$. If its temperature coefficient of resistance be $0.005$ per ${}^{\circ }\text{C}$, its resistance will become $200\Omega$ at a temperature of:

An electric bulb is rated $220\text{V}-100\text{W}$. The power consumed by it when operated on $110\text{V}$ will be:

An inductor ($L=100\text{mH}$), a resistor ($R=100\Omega$) and a battery ($E=100\text{V}$) are connected in series. After a long time, the battery is disconnected after short-circuiting. The current in the circuit $1\text{ms}$ after the short-circuit is:

Current $I$ enters at point A and leaves at point D of a conducting block. To find the voltage $\Delta V$ between points B and C, we assume current spreads over a hemispherical surface. The electric field at distance $r$ is $E=\rho j$. The potential difference $V_B-V_C$ is:

A $5\text{V}$ battery ($2\Omega$ internal resistance) and a $2\text{V}$ battery ($1\Omega$ internal resistance) are connected in parallel to a $10\Omega$ resistor. The current in the $10\Omega$ resistor is:

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1: The temperature dependence of resistance is usually given as $R=R_0(1+\alpha \Delta t)$. The resistance of a wire changes from $100\Omega$ to $150\Omega$ when its temperature is increased from $27^{\circ }\text{C}$ to $227^{\circ }\text{C}$. This implies that $\alpha =2.5\times 10^{-3}{/}^{\circ }\text{C}$.
Statement 2: $R=R_i(1+\alpha \Delta T)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=(R-R_0)\ll R_0$.

Two conductors have the same resistance at $0^{\circ }\text{C}$ but their temperature coefficients of resistance are ${\alpha }_1$ and ${\alpha }_2$. The respective temperature coefficients of their series and parallel combinations are nearly:

A resistor $R$ and $2\mu \text{F}$ capacitor in series is connected through a switch to $200\text{V}$ direct supply. Across the capacitor is a neon bulb that lights up at $120\text{V}$. Calculate the value of $R$ to make the bulb light up $5\text{s}$ after the switch has been closed. (${\log }_{10}2.5=0.4$)

If a wire is stretched to make it $0.1\%$ longer, its resistance will:

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between:(Note: Graph shows $V=25$ at $t=0$, $V\approx 12.5$ at $t=100$, $V\approx 6.25$ at $t=200$)

The length of a given cylindrical wire is increased by $100\%$. Due to the consequent decrease in diameter, the percentage change in the resistance of the wire will be:

Two electric bulbs marked $25\text{W}-220\text{V}$ and $100\text{W}-220\text{V}$ are connected in series to a $440\text{V}$ supply. Which of the bulbs will fuse?

Shown in the figure is a meter-bridge setup with null deflection in the galvanometer. One resistor is $55\Omega$ and the balancing length from left is $20\text{cm}$. The value of the unknown resistor $R$ on the right side is:

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is:

The thermo e.m.f. of a thermo-couple is $25\mu {\text{V/}}^{\circ }\text{C}$ at room temperature. A galvanometer of $40\Omega$ resistance, capable of detecting current as low as $10^{-5}\text{A}$, is connected with the thermocouple. The smallest temperature difference that can be detected by this system is:

A strip of copper and another of germanium are cooled from room temperature to $80\text{K}$. The resistance of:

A $220\text{volt}$, $1000\text{watt}$ bulb is connected across a $110\text{volt}$ mains supply. The power consumed will be:

The length of a wire of a potentiometer is $100\text{cm}$, and the e.m.f. of its standard cell is $E$ volt. It is employed to measure the e.m.f. of a battery whose internal resistance is $0.5\Omega$. If the balance point is obtained at $l=30\text{cm}$ from the positive end, the e.m.f. of the battery is:

A $3\text{V}$ battery with negligible internal resistance is connected in a circuit as shown. (Circuit consists of three $3\Omega$ resistors, two in parallel, then in series with the third). The current $I$ in the circuit will be:

An ammeter reads up to $1\text{A}$. Its internal resistance is $0.81\Omega$. To increase the range to $10\text{A}$, the value of the required shunt is:

The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the: