A circuit consists of three batteries of emf | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The batteries are connected in parallel. The equivalent emf $E_{eq}$ and equivalent internal resistance $r_{eq}$ of the combination are given by:$

Vedclass · Accepted Answer

$2.0$

Vedclass · Answer

(B) The batteries are connected in parallel. The equivalent emf $E_{eq}$ and equivalent internal resistance $r_{eq}$ of the combination are given by:$E_{eq} = \frac{\frac{E_{1}}{r_{1}} + \frac{E_{2}}{r_{2}} + \frac{E_{3}}{r_{3}}}{\frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}}}$$\frac{1}{r_{eq}} = \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}}$Given $E_{1} = 1 	ext{ V}, r_{1} = 1 \Omega$; $E_{2} = 2 	ext{ V}, r_{2} = 2 \Omega$; $E_{3} = 3 	ext{ V}, r_{3} = 1 \Omega$.First, calculate the equivalent internal resistance:$\frac{1}{r_{eq}} = \frac{1}{1} + \frac{1}{2} + \frac{1}{1} = 1 + 0.5 + 1 = 2.5 \Omega^{-1} = \frac{5}{2} \Omega^{-1}$$r_{eq} = \frac{2}{5} \Omega = 0.4 \Omega$Now, calculate the equivalent emf:$E_{eq} = r_{eq} 	imes \left( \frac{E_{1}}{r_{1}} + \frac{E_{2}}{r_{2}} + \frac{E_{3}}{r_{3}} ight)$$E_{eq} = 0.4 	imes \left( \frac{1}{1} + \frac{2}{2} + \frac{3}{1} ight) = 0.4 	imes (1 + 1 + 3) = 0.4 	imes 5 = 2.0 	ext{ V}$Thus, the potential difference between points $P$ and $Q$ is $2.0 	ext{ V}$.

Similar Questions

Explain cell,emf,and internal resistance. Derive the relation between potential difference,emf,and internal resistance.

Four identical cells of emf $E$ and internal resistance $r$ are to be connected in series. If one of the cells is connected wrongly,the equivalent emf and effective internal resistance of the combination are

Two cells,each of $e.m.f. \ E$ and internal resistance $r$,are connected in parallel across an external resistor $R$. If the power delivered to the resistor $R$ is maximum,then:

If six identical cells each having an $e.m.f.$ of $6\,V$ are connected in parallel,the $e.m.f.$ of the combination is ................ $V$.

For a cell with non-zero (finite) internal resistance,write the relation between the terminal voltage $(V)$ and the electromotive force $(E)$ of the cell.

Vedclass Test Series

Exam Paper Generator

Online Exam Module