Question

How many electric bulbs connected in parallel and each rated at \[50\,W\] and \[100\,V\] can burn at full power when connected to an accumulator battery with an electromotive force of \[120\,V\] and an internal resistance of \[10\Omega \] ?

Answer 1

Hint:In electricity, resistance is a property of an electric circuit or a component of an electric circuit that converts electrical energy into heat energy in the presence of an opposing electric current. Collisions of current-carrying charged particles with fixed particles that make up the conductor structure cause resistance. Resistance is typically thought to be confined in devices where it predominates, such as lamps, heaters, and resistors, despite the fact that it is present in every portion of a circuit, including connecting wires and electric transmission lines.

Complete step by step answer:
A parallel circuit has branches that divide the current so that just a portion of it passes through each branch. In a parallel circuit, the voltage, or potential difference, between each branch is the same, but the currents may differ.

Now, let us come to the question; each bulb's resistance and current requirements are shown below.
${R_1} = \dfrac{{{V^2}}}{N}\,and\,{I_1} = \dfrac{N}{V}$
Where \[N\] is the bulb's rated power. When m bulbs are linked in series, the circuit's exterior resistance is \[R{\text{ }} = {\text{ }}\dfrac{{{R_1}}}{m}{\text{ }} = {\text{ }}\dfrac{{{V_2}}}{{Mn}}\] . The current in the circuit should be sufficient to maintain the lamps' usual power.
$I = m{I_1} = \dfrac{{mN}}{V}$

Inserting the equation for $R$ and $I$ in the equation for Ohm’s law for the entire circuit, we obtain
$\varepsilon = I\left( {R + r} \right) = \dfrac{{mN}}{V}\left\{ {\dfrac{{{V^2}}}{{mN}} + r} \right\} $
Where, ‘$r$’ is the internal resistance of the battery. Therefore
$m = \dfrac{{\left( {\varepsilon - V} \right)}}{{Nr}} \\
\therefore m= 4$

Therefore, 4 electric bulbs connected in parallel.

Note: When the temperature of a conductor, or circuit element, rises, the resistance of that conductor or circuit element rises as well. Some conductors exhibit zero resistance when cooled to extremely low temperatures. After the applied electromotive force is removed, currents continue to flow in certain substances, known as superconductors.