Question

find the resultant potential difference from the given figure based on loop law.find the current in the circuit when R1 =2ohm; R2=4ohm,R3=3ohm,V1=6VandV2=12V.

Answer 1

The resultant potential difference from the given figure based on loop law is zero V

The current in the given circuit is 2 A

Given,

Resistance of first resistor, R1 = 2 ohm

Resistance of second resistor, R2 = 4 ohm

Resistance of third resistor, R3 = 3 ohm

The voltage of the first cell, V1 = 6 V

The voltage of the second cell, V2 = 12 V

To Find,

1) the resultant potential difference from the given figure based on loop law

2) the current in the circuit

Solution,

1) The resultant potential difference from the given figure can be obtained by using the loop law or the Kirchhoff's second rule or the Kirchhoff's loop rule

According to Kirchhoff's second rule - the loop rule,

"The algebraic sum of changes in potential around any closed circuit path (loop) must be zero"

i.e., ∑V=0

here, V1 - IR3 + V2 - IR2 - IR1 = 0

Therefore, the resultant potential difference from the given figure based on loop law is zero V

2) To find the current in the circuit, we again use Kirchhoff's loop rule.

Since the resultant potential difference of the circuit in the given figure which forms a loop is zero, we have the following equation:

$V_1 - IR_3 + V_2 - IR_2 - IR_1 = 0$

Note that the positive and negative signs assigned to each quantity are important. Let us move in the same direction as the current given in this loop.

The potential difference in V1 and V2 is from negative to the positive terminal, and hence has a positive sign

The potential difference in R1, R2, and R3 is in the same direction as the current, and hence has a negative sign (potential difference of a resistor v=ir where i is the current passing through it and r is its resistance)

Now, substitute the given values of R1, R2, R3, V1, and V2 in the above equation to obtain the value of the current I

⇒ $6 - 3*I + 12 - 4*I - 2*I = 0$

⇒ $18 - 9*I = 0$

⇒ $9*I = 18$

⇒ $I = 2 A$

Therefore, the current in the given circuit is 2 A

Answer 2

The resulting potential difference and current are 0 and 2A respectively.

Given:

R1 =2ohm; R2=4ohm, R3=3ohm, V1=6VandV2=12V.

To Find:

The potential difference and the current in the circuit.

Solution:

To find the potential difference and the current we will follow the following step:

According to Kirchoff's loop rule: the sum of changes in potential difference across the circuit is 0.

ΣV=0

Hence, the resulting potential difference will be 0.

So,

V1 - IR3 + V2 - IR2 - IR1 = 0

V1 and V2 are taken positively as potential differences can be calculated from the negative to the positive terminal.

Also, V = IR

In all the three resistor potential differences and the current is in the same direction. so, the potential is taken negatively.

Now,

Putting values in the above equation we get,

6 - 3I + 12 - 4I - 2I = 0

18 - 9I = 0

9I = 18

I =

$\frac{18}{9} = 2A$

Henceforth, the resulting potential difference and current are 0 and 2A respectively.

Project code- #SPJ3