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A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2\, L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. the value of $N$ is
A heater coil connected to a supply of a $220\, V$ is dissipating some power ${P_1}.$ The coil is cut into half and the two halves are connected in parallel. The heater now dissipates a power ${P_2}.$ The ratio of power ${P_1}\,\,:\,\,{P_2}$ is
For comparing the $e.m.f.$'s of two cells with a potentiometer, a standard cell is used to develop a potential gradient along the wires. Which of the following possibilities would make the experiment unsuccessful
A student was trying to construct the circuit shown in the figure below marked $(a)$, but ended up constructing the circuit marked $(b)$. Realising her mistake, she corrected the circuit, but to her surprise, the output voltage (across $R$ ) did not change. The value of resistance $R$ is ............ $\Omega$
In the circuit shown, the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $1\,\Omega $ and the ideal cell has an $e.m.f.$ $10\, V$. Then, the Ammeter has a coil resistance equal to ............... $\Omega$