Kirchhoff's Laws and Their Applications

Which of the following rule may be used to obtain the values of the three unknown currents in the branches (shown) of the circuit given below?

Apply Kirchhoff’s rule to the loops $PRSP$ and $PRQP$ to find currents  $I_1,I_2$  and  $I_3$  in the network.

Apply Kirchhoff’s rules to the loops $ACBPA$ and $ACBQA$ to write the expressions for the currents  $I_1, I_2$  and  $I_3$  in the network.

State Kirchhoff’s rules. Use these rules to write the expressions for the currents  $I_1, I_2$ and $I_3$ in the circuit diagram shown.

Explain Kirchhoff's laws with examples.

A battery of internal resistance $4 \mathrm{\Omega }$ is connected to the network of resistances, as shown in the figure. In order that the maximum power can be delivered to the network, the value of $\mathrm{R}$ in $\mathrm{\Omega }$ should be

In the circuit shown in the figure. $\left(\mathrm{A}\right)$, $R_3$ is a variable resistance



As the value $R_3$ is changed, current $I$ though the cell varies as shown. Obviously, the variation is asymptotic, i.e. $I\mathrm{ }\to \mathrm{ }6 \mathrm{A}$ as $R_3\to \mathrm{\infty }$ . Ratio of resistances $R_1 \text{and} R_2$ will be: 

As the switch $S$ is closed in the circuit, the current passed through it is (in $\mathrm{A}$)

Four resistances $40\mathrm{\Omega }, 60\mathrm{\Omega }, 90\mathrm{\Omega }$ and $110\mathrm{\Omega }$ make the arms of a quadrilateral $ABCD.$ Across $AC$ is a battery of emf $40 V$ and internal resistance negligible. The potential difference across $BD$ in $V$ is __________ .

In the circuit shown in the figure, reading of voltmeter is $V_1$ when $S_1$ is closed, reading of voltmeter is $V_2$ when only $S_2$ is closed and reading of voltmeter is $V_3$ when both $S_1$ and $S_2$ are closed. Then -

The series combination of two batteries, both of the same emf $10 \mathrm{V},$ but different internal resistance of $20 \mathrm{\Omega }$ and $5\mathrm{\Omega },$ is connected to the parallel combination of two resistors $30\mathrm{\Omega }$ and $\mathrm{R\Omega }.$ The voltage difference across the battery of internal resistance $20 \mathrm{\Omega }$ is zero, the value of $\mathrm{R}($ in $\mathrm{\Omega })$ is......

In the shown circuit the resistance $R$ can be varied

The variation of current through $R$ against $R$ is correctly plotted as:

In the circuit shown, the value of $R$ in ohm that will result in no current through the $30 \mathrm{V}$ battery, is:

Kirchhoff's first law and second law, proves the

The box in the circuit below has two inputs marked $v_{+}$ and $v_{-}$ and a single output marked $V_0.$ The output obeys

$V_0=+10V$, if $v_{+}>v_{-}$

$V_0=$$-10V$, if $v_{+}<v_{-}$

The output $V_0$ of this circuit a long time after it is switched on is best represented by:

A student was trying to construct the circuit shown in the figure below marked (a), but ended up constructing the circuit marked (b). Realizing her mistake, she corrected the circuit, but to her surprise, the output voltage (across $R$) did not change.

The value of resistance $R$ is :-

Consider the part of the circuit shown. What is the value of current $I,$ if the battery is ideal?

Kirchhoff's first law is based on conservation of

Kirchhoff’s second law states that the total sum of currents entering into a node is zero.