Question

Find the current through R₃ in the circuit as shown in figure?

• A. 2A
• B. 3A
• C. 3.5A
• D. 2.5A

Answer 1

The correct option is D 2.5A

Yeah that’s right! The cells are in parallel (with same polarity) obviously. Let’s try to find the equivalent EMF and resistance of a single cell which can replace the above combination.
$E=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}E=\frac{10\times 10+20\times 5}{10+5}=\frac{40}{3}Vr=\frac{10\times 5}{10+5}=\frac{10}{3}\Omega$
Now just consider this single cell attached to a 2 $\Omega$ resistor in a simple circuit.
$R_{eq}=\frac{10}{3+2}=\frac{16}{3}\Omega E=\frac{40}{3}Vi=\frac{E}{R_{eq}}=2.5A$