Question
Write and explain Kirchhoff's junction rule.
✓
Answer
→Kirchhoff's junction rule : "At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction."
→ Consider junction O of a network as shown in the figure.
→The currents meeting at the junction point O are $I _1, I _2, I _3, I _4$ and $I _5$ respectively. Their directions are represented by arrows in the figure.
→Let $Q_1, Q_2, Q_3, Q_4$, and $Q_5$ be charges flowing through the cross- sectional area of conductors at time $t$ respectively.
→Thus,
$\begin{array}{l}
I _1=\frac{ Q _1}{t} \quad \therefore Q _1= I _1 t \\
I _2=\frac{ Q _2}{t} \quad \therefore Q _2= I _2 t \ldots \\
I _3=\frac{ Q _3}{t} \quad \therefore Q _3= I _3 t \\
I _4=\frac{ Q _4}{t} \quad \therefore Q _4= I _4 t \\
I _5=\frac{ Q _5}{t} \quad \therefore Q _5= I _5 t
\end{array}$
→From the figure, the total electric charge entering the junction is $Q_1+Q_3$ while $Q_2+Q_4+Q_5$ amount of electric charge is leaving the junction in time $t$.
→According to the law of conservation of charge,
$\begin{array}{ll}
& Q _1+ Q _3= Q _2+ Q _4+ Q _5 \\
\therefore & I _1 t+ I _3 t= I _2 t+ I _4 t+ I _5 t \\
\therefore & I _1+ I _3= I _2+ I _4+ I _5
\end{array}$
→Thus at the junction the sum of the currents entering the junction is equal to the sum of currents leaving the junction.
→ Consider junction O of a network as shown in the figure.
→The currents meeting at the junction point O are $I _1, I _2, I _3, I _4$ and $I _5$ respectively. Their directions are represented by arrows in the figure.
→Let $Q_1, Q_2, Q_3, Q_4$, and $Q_5$ be charges flowing through the cross- sectional area of conductors at time $t$ respectively.
→Thus,
$\begin{array}{l}
I _1=\frac{ Q _1}{t} \quad \therefore Q _1= I _1 t \\
I _2=\frac{ Q _2}{t} \quad \therefore Q _2= I _2 t \ldots \\
I _3=\frac{ Q _3}{t} \quad \therefore Q _3= I _3 t \\
I _4=\frac{ Q _4}{t} \quad \therefore Q _4= I _4 t \\
I _5=\frac{ Q _5}{t} \quad \therefore Q _5= I _5 t
\end{array}$
→From the figure, the total electric charge entering the junction is $Q_1+Q_3$ while $Q_2+Q_4+Q_5$ amount of electric charge is leaving the junction in time $t$.
→According to the law of conservation of charge,
$\begin{array}{ll}
& Q _1+ Q _3= Q _2+ Q _4+ Q _5 \\
\therefore & I _1 t+ I _3 t= I _2 t+ I _4 t+ I _5 t \\
\therefore & I _1+ I _3= I _2+ I _4+ I _5
\end{array}$
→Thus at the junction the sum of the currents entering the junction is equal to the sum of currents leaving the junction.
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