Question

Three identical cells, each of emf. 2v and unknown internal resistance are connectedin parallel .This combination is connected to a 5ohm resister. If the terminal voltage across

the cell is 1.5volt. What is the internal resistance of each cell .

Answer 1

According to the question net emf of the circuit is equivalent single cell = 2V , now three resistor of resistancer is connected in parallel and the combination is connected in series with 5$\Omega$ resitor , now net resistance of the circuit will be
$$\begin{gathered} \frac{1}{r_{combination}}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}=\frac{3}{r} \\ {r}_{combination}=\frac{r}{3} \\ and{R}_{net}=r_{combination}+5=\frac{r}{3}+5.........1> \end{gathered}$$
now the current in the circuit will be
i = E/R_net
= $\frac{2}{{\displaystyle \frac{r}{3}}+5}$ ........eq ..........2> using equation 1>
now the formula of terminal voltage is
V = E -ir
$$\begin{gathered} 1.5=2-\frac{2r}{{\displaystyle \frac{r}{3}}+5} \\ \frac{2r}{{\displaystyle \frac{r}{3}}+5}=0.5 \\ \frac{6r}{{\displaystyle r}+15}=0.5 \\ 12r=r+15 \\ 11r=15 \\ r=\frac{15}{11}\Omega \end{gathered}$$
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