Current Electricity and Electrical InstrumentMedium

Question

The voltage and the current between A and B points shown in the circuit are $\_\_\_\_$ .

Options

A.$24\text{ }V,12\text{ }A$
B.$24\text{ }V,4\text{ }A$
C.$18\text{ }V,12\text{ }A$
D.$27\text{ }V,4\text{ }A$

Solution

Sol. [Key Concept: Combine the parallel EMF branches: $E_{eq} = \frac{\sum\ E/r}{\sum\ 1/r}$, $r_{eq}$; then $i$ and $V_{AB} = iR$.]

This circuit can be

Here : $E_{\text{eq}\text{~}} = \frac{\frac{27}{3} + \frac{27}{3} + \frac{27}{3} + \frac{27}{3}}{\frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3}}$

$${E_{eq} = 27\text{ }V }{r_{\text{eq}\text{~}} = \frac{3}{4}\Omega }{i_{\text{AB}\text{~}} = \frac{27}{6 + \frac{3}{4}} = 4\text{ }A }$$$V_{AB} = 4 \times 6 = 24$ Volt

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