MODEL QUESTIONS (IPE PATTERN)

Two $120 \mathrm{V}$ light bulbs, one of $25 \mathrm{W}$ and another of $200 \mathrm{W}$ are connected in series. One bulb burnt out instantaneously. Which one was burnt and why?

A cylindrical metallic wire is stretched to increase its length by $5\%$. Calculate the percentage change (in $\%$) in resistance.

Two wires $A$ and $B$ of same length and same material, have their cross-sectional areas in the ratio $1:4$. What would be the ratio of heat produced in these wires when the voltage across each is constant?

Two bulbs whose resistances are in the ratio of $1:2$ are connected in parallel to a source of constant voltage. What will be the ratio of power dissipation in these?

A potentiometer wire is $5 \mathrm{m}$ long and a potential difference of $6 \mathrm{V}$ is maintained between its ends. Find the emf (in $\mathrm{V}$) of a cell which balances against a length of $180 \mathrm{cm}$ of the potentiometer wire.

A battery of emf $2.5 \mathrm{V}$ and internal resistance $r$ is connected in series with a resistor of $45$ ohm through an ammeter of resistance $1$ ohm. The ammeter reads a current of $50 \mathrm{mA}$. Draw the circuit diagram and calculate the value of $r$.

Amount of charge passing through the cross-section of a wire is $q\left(t\right)=a{t}^2+bt+c$. Write the dimensional formula for $a$, $b$ and $c$. If the values of $a$, $b$ and $c$ in SI unit are $6$, $4$, $2$ respectively, find the value of current at $t=6$ seconds.

A potentiometer circuit for comparison of two resistances is shown below. The balance point with a standard resistor $R=10.0 \Omega$ is found to be $58.3 \mathrm{cm}$, while that with the unknown resistance $X$ is $68.5 \mathrm{cm}$. Determine the value of $X$. What might you do if you failed to find a balance point with the given cell of emf  $\epsilon$.