Question 100: Current Electricity

Question

In the given circuit, the current flowing through the resistance $$20 \Omega$$ is $$0.3 \mathrm{~A}$$, while the ammeter reads $$0.9 \mathrm{~A}$$. The value of $$\mathrm{R}_1$$ is _________ $$\Omega$$.

Accepted Answer

Given, $$\mathrm{i}_1=0.3 \mathrm{~A}, \mathrm{i}_1+\mathrm{i}_2+\mathrm{i}_3=0.9 \mathrm{~A}$$
So, $$\mathrm{V}_{\mathrm{AB}}=\mathrm{i}_1 	imes 20 \Omega=20 	imes 0.3 \mathrm{~V}=6 \mathrm{~V}$$
$$\begin{aligned}
& \mathrm{i}_2=\frac{6 \mathrm{~V}}{15 \Omega}=\frac{2}{5} \mathrm{~A} \
& \mathrm{i}_1+\mathrm{i}_2+\mathrm{i}_3=\frac{9}{10} \mathrm{~A} \
& \frac{3}{10}+\frac{2}{5}+\mathrm{i}_3=\frac{9}{10} \
& \frac{7}{10}+\mathrm{i}_3=\frac{9}{10} \
& \mathrm{i}_3=0.2 \mathrm{~A} \
& \mathrm{So}, \mathrm{i}_3 	imes \mathrm{R}_1=6 \mathrm{~V} \
& (0.2) \mathrm{R}_1=6 \
& \mathrm{R}_1=\frac{6}{0.2}=30 \Omega
\end{aligned}$$

Current Electricity

In the given circuit, the current flowing through the resistance $20 \Omega is 0.3 \mathrm{~A}, while the ammeter reads 0.9 \mathrm{~A}. The value of \mathrm{R}_1 is _________ \Omega$.

Integer / Numeric Answer Type