Name: Meter Bridge
Uploaded: 2019-07-19
Duration: 7 min 2 s
Description: Measurement, by comparison, is always accurate. The video talks about a metre bridge device that helps us find the unknown resistance by comparing it with a...

Question

Using Kirchhoff $'$ s rules, calculate the current through the $40 Ω$ and $20 Ω$ resistors in the following circuit $:$

Accepted Answer

According to Kirchhoff $'$ s voltage rule the algebraic sum of the changes in the potential around any closed loop must be zero.

Applying Kirchhoff $20 Ω$ s voltage rule in the loop $ABCDA$ :

$80 - 20 i_{1} - 40 (i_{1} - i_{2}) = 0 \Rightarrow 80 - 60 i_{1} + 40 i_{2} = 0 \Rightarrow 4 - 3 i_{1} + 2 i_{2} = 0 — equation (I)$

Now applying Kirchhoff $'$ s voltage rule in the loop $FEDCF :$

$40 + 40 (i_{1} - i_{2}) - 10 i_{2} = 0 \Rightarrow 40 + 40 i_{1} - 50 i_{2} = 0 \Rightarrow 4 + 4 i_{1} - 5 i_{2} = 0 — equation (II)$

Multiplying equation $(I)$ by $4$ and equation $(II)$ by $3$ and then adding both the equations, we get

$4 (4 - 3 i_{1} + 2 i_{2}) + 3 (4 + 4 i_{1} - 5 i_{2}) = 0 \Rightarrow 28 - 7 i_{2} = 0 \Rightarrow i_{2} = 4 A$

Substitute $i_{2} = 4$ in equation $(I)$ , we get

$4 - 3 i_{1} + 2 \times 4 = 0 \Rightarrow i_{1} = 4 A$

So, current passing through $40 Ω$ resistor is $= i_{1} - i_{2} = 4 - 4 = 0 A$ .

So, there will be no current through $40 Ω$ resistor.

And, current passing through the $20 Ω$ resistor is $4 A$ .

Using Kirchhoff $'$ s rules, calculate the current through the $40 Ω$ and $20 Ω$ resistors in the following circuit $:$

Important Questions on Current Electricity

Learn and Prepare for any exam you want !

Using Kirchhoff's rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit:

Important Questions on Current Electricity

Learn and Prepare for any exam you want !

Using Kirchhoff $'$ s rules, calculate the current through the $40 Ω$ and $20 Ω$ resistors in the following circuit $:$