Current Electricity — Physics STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 SciencePhysicsCurrent Electricity5 Marks
Question
For the circuit shown here, calculate the potential difference between points B and D.
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Answer
According to Kirchhoff’s first law the distribution of currents is shown in fig.
Applying Kirchhoff’s second law to mesh BADB, –2(i – i1) +2 – 1 – 1. (i – i1) + 2i1 = 0 ⇒ 3i – 5i1 = 1 …(i) Applying Kirchhoff’s law to mesh DCBD, -3i + 3 - 1 - 1× i - 2i1 = 0 ⇒ 4i + 2i1 = 2 Or 2i + i1 = 1 …(ii) Multiplying equation (ii) with 5, we get 10i + 5i1 = 5 …(iii) Adding (i) and (iii), we get $13\text{i}=6\Rightarrow\text{i}=\frac{6}{13}\text{A}$ From (ii), $\text{i}_1=1-2\text{i}=1-\frac{12}{13}=\frac{1}{13}\text{A}$ Potential difference between B and D is, $\text{V}_\text{n}-\text{v}_\text{n}=\text{i}-1\times2=\frac{2}{13}\text{V}$
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