Question

A generator has an e.m.f. of $440\,\,V$ and internal resistance of 4 $400\,\,\Omega$. Its terminals are connected to a load of $4000\,\,\Omega$. The voltage across the load is:
A) $220\,\,V$.
B) $440\,\,V$.
C) $200\,\,V$.
D) $400\,\,V$.

Answer 1

We can solve this problem using the formula that is given by Ohm's law, which consists of the current that is flowing through the circuit, the potential difference across the circuit and the resistance of the material.

Formula Used:
By the formula from Ohm’s law
$V = IR$
Where, $V$ denotes the potential difference across the load, $I$ denotes the current across the load, $R$ denotes the resistance across the load.

Complete step by step answer:
The data given in the problem is;
E.M.F of a generator, $V = 440\,\,V$,
Internal resistance of the generator, ${R_i} = 400\,\,\Omega$,
Resistance of the load, ${R_L} = 4000\,\,\Omega$

By ohm’s law;
$V = IR$
The total resistance can be calculated by;
$R = {R_i} + {R_L}$
Where, $R$ denotes the total resistance, ${R_i}$ denotes the internal resistance, ${R_L}$ denotes the resistance of the load.
Substitute the values of ${R_i}$ and ${R_L}$;
$R = 400\,\,\Omega + 4000\,\,\Omega$
$R = 4400\,\,\Omega$
The total resistance is $R = 4400\,\,\Omega$.
To calculate the flow of current, by Ohm’s law;
$I = \dfrac{V}{R}$
Substitute the value of $V$ and total resistance $R$;
$I = \dfrac{{440\,\,V}}{{4400\,\,\Omega }}$
$I = 0.1\,\,A$
the flow of current $I = 0.1\,\,A$

Now to find the voltage across the load, by Ohm’s law;
${V_L} = {R_L} \times I$
Where, ${V_L}$ denotes the voltage across the load, ${R_L}$ denotes the resistance of the load.
Substitute the values of ${R_L}$ and $I$,
${V_L} = 4000\,\,\Omega \times 0.1\,\,A$
${V_L} = 400\,\,V$.
Therefore, the voltage across the load is ${V_L} = 400\,\,V$.

Hence, the option (D) ${V_L} = 400\,\,V$ is the correct answer.

Note: In part for finding the voltage across the load ${V_L}$ we only have to take the resistance that is present across the load that is ${R_L}$ and not the total resistance $R$, because we only have to find the voltage that acts across the load.