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.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An immersion heater rated 1000W, 220V is used to heat 0.01m3 of water. Assuming that the power is supplied at 220V and 60% of the power supplied is used to heat the water, how long will it take to increase the temperature of the water from 15°C to 40°C?
Find the intensity at a point on a screen in Young’s double slit experiment where the interfering waves have a path difference of (i) $\lambda/6$, and (ii) $\lambda/2.$
→Calculate the electric flux passing through the spheres $S_1$ and $S_2$ shown in the figure. The linear charge density of the wire $A B$ shown in the figure is $\lambda=K x$ where $x=$ distance from the end $A$ of the wire measured along its length.
→The eyepiece of an astronomical telescope has a focal length of 10cm. The telescope is focused for normal vision of distant objects when the tube length is 1.0m. Find the focal length of the objective and the magnifying power of the telescope.
Protons with kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field, so that it just misses a plane target kept at a distance l in front of the accelerator. Find the magnetic field.
An inductor-coil carries a steady-state current of 2.0A when connected across an ideal battery of emf 4.0V. If its inductance is 1.0H, find the time constant of the circuit.
Draw $ৎ \rightarrow$ T graph for metals, alloys and semi conductor and explain.
→Explain the first law of reflection of light.
Answer the following questions:
A high tension (HT) supply of, say, 6 kV must have a very large internal resistance. Why?
A high tension (HT) supply of, say, 6 kV must have a very large internal resistance. Why?
Write the uses of Gauss's law.