Current Electricity Set-2

Q1. A cell of emf $12\ \text{V}$ and internal resistance $1\ \Omega$ is connected to an external resistor $R=3\ \Omega$. What fraction of the total power supplied by the cell is dissipated inside the cell (i.e., in its internal resistance)?

Q2. A resistor $R$ is measured using an ammeter (internal resistance $r_A=1.0\ \Omega$) placed in series and a voltmeter (internal resistance $R_V=200\ \Omega$) connected across the resistor. A battery of emf $10\ \text{V}$ (negligible internal resistance) is used. With the instruments connected in the usual way the ammeter reads $0.50\ \text{A}$ and the voltmeter reads $9.50\ \text{V}$. The true resistance $R$ is approximately:

Q3. Assertion (A): The electrical conductivity of a metal decreases with increase in temperature.
Reason (R): The number density of conduction electrons in a metal decreases with increasing temperature.

Q4. A uniform wire of length $1.00\ \text{m}$ and uniform cross-sectional area is connected across an ideal $10\ \text{V}$ battery. A segment of length $0.20\ \text{m}$ is replaced by another wire of the same cross-section but with resistivity twice that of the original wire. The $V$–$x$ (potential vs distance) graph along the wire becomes piecewise linear. The potential difference across the replaced $0.20\ \text{m}$ segment is:

Q5. A copper wire of length $2.0\ \text{m}$ and cross-sectional area $0.50\ \text{mm}^2$ has resistivity $1.6\times 10^{-8}\ \Omega\cdot\text{m}$. The resistance of the wire is:

Q6. Assertion (A): For a battery of emf $E$ and internal resistance $r$, if the external load resistance $R$ is increased, the power dissipated in the load always increases.
Reason (R): The terminal voltage across the load increases as the load resistance increases.

Q7. Two identical incandescent bulbs, each of resistance $R$, are connected in series across a battery (emf $E$, internal resistance negligible). A third identical bulb is then connected in parallel with one of the two bulbs (so the circuit becomes: one bulb in series with a parallel pair of two identical bulbs). Immediately after this connection, what is the ratio of the power dissipated in the single series bulb to the power dissipated in each bulb of the parallel pair?

Q8. The $V$–$I$ characteristic of a two-terminal device passes through the origin and is smooth and concave upward (i.e. $d^2V/dI^2>0$). At a point $P$ on the curve define static resistance $R_s=\dfrac{V}{I}$ and dynamic (differential) resistance $r_d=\dfrac{dV}{dI}$ at $P$. Which of the following is correct at $P$?

Q9. Assertion (A): For a wire carrying a fixed current $I$, the drift speed $v_d$ of electrons is inversely proportional to its cross-sectional area $A$.
Reason (R): $v_d=\dfrac{I}{n e A}$ where $n$ is the number density of conduction electrons and $e$ is the electron charge.

Q10. Consider an infinite ladder network built from identical resistors $R=10\ \Omega$ where each repeating section consists of a resistor $R$ in series followed by a resistor $R$ placed in parallel with the rest of the infinite network. If $x$ is the equivalent resistance seen at the input of the infinite network, then $x$ satisfies $x=R+\dfrac{Rx}{R+x}$. The numerical value of $x$ (in $\Omega$) is approximately: