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

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 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

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 :-

Kirchhoff's first law is based on conservation of

Find the magnitude of flowing current in $R_2$ of following circuit, when a constant voltage $22 V$ is kept between $AB.$

A $6 V$ cell with $1 \mathrm{\Omega }$ internal resistance and $10 V$ cell with $2 \mathrm{\Omega }$ internal resistance and $10 \mathrm{\Omega }$ external resistance are connected in parallel. The current in ampere through $10 V$ cell is

Consider the circuit as shown below. In the circuit $R_1=R_2=R_3=4 \mathrm{\Omega }, V_1=10 \mathrm{V}$ and $V_2=5 \mathrm{V}.$ The current flowing through resistance $R_3$ is

Find the current I in the circuit below that flows through $20 \mathrm{\Omega }$ resistor.

For what value of $R$ in the circuit as shown, the current through $4 \mathrm{\Omega }$ will be zero ?