Find the equivalent resistance between AB AC and AD

### Asked by megha.chhoti1456 | 2nd Aug, 2021, 08:53: PM

Expert Answer:

###
Let us name the resistors R_{1 },_{ }R_{2} ................... R_{8 }as shown in figure .
--------------------------------------------------------------------
Equivalent resistance between A and B :-
Resistors R_{3 }and R_{8} are redundant to get equivalent resistance between A and B .
Hence , they are removed in Step-1 as shown below
Now R_{2 }, R_{5} and R_{7} are in series and equivalenet resistance of this series combination is 6 Ω .
Hence in step-2 , this series combination is replaced by 6 Ω resistor .
Now resistor R_{4} is in parallel with 6 Ω resistor,
Equivalenet resistance of parallel combination is ( 2 × 6 ) / (2+6) = 1.5 Ω .
Hence, finally, resistance between A and B is ( 2 + 1.5 + 2 ) = 5.5 Ω .
-----------------------------------------------------------------------------------------------------
Equivalent resistance between A and C :-
Resistors R_{6 }and R_{8} are redundant to get equivalent resistance between A and C .
Hence , they are removed in Step-1 as shown below
Now R_{4 }, R_{5} and R_{7} are in series and equivalenet resistance of this series combination is 6 Ω .
Hence in step-2 , this series combination is replaced by 6 Ω resistor .
Now resistor R_{2} is in parallel with 6 Ω resistor,
Equivalenet resistance of parallel combination is ( 2 × 6 ) / (2+6) = 1.5 Ω .
Hence, finally, resistance between A and C is ( 2 + 1.5 + 2 ) = 5.5 Ω .
--------------------------------------------------------------------------------------------------------
Equivalent resistance between A and D :-
Resistors R_{6 }and R_{3} are redundant to get equivalent resistance between A and D .
Hence , they are removed in Step-1 as shown below
R_{2} and R_{5} are in series . Similarly R_{4} and R_{7} are in series .
Series combination of R_{2} and R_{5} , i.e., 4 Ω is in parallel to series combination of R_{4} and R_{7} which is 4 Ω .
Hence two parallel 4 Ω resistors gives equivalenet resistance 2 Ω as shown in step-2 and step-3 .
Effective resistance between A and D is ( 2 + 2 + 2 ) Ω = 6 Ω

Let us name the resistors R

_{1 },_{ }R_{2}................... R_{8 }as shown in figure .--------------------------------------------------------------------

Equivalent resistance between A and B :-

Resistors R

_{3 }and R_{8}are redundant to get equivalent resistance between A and B .Hence , they are removed in Step-1 as shown below

Now R

_{2 }, R_{5}and R_{7}are in series and equivalenet resistance of this series combination is 6 Ω .Hence in step-2 , this series combination is replaced by 6 Ω resistor .

Now resistor R

_{4}is in parallel with 6 Ω resistor,Equivalenet resistance of parallel combination is ( 2 × 6 ) / (2+6) = 1.5 Ω .

Hence, finally, resistance between A and B is ( 2 + 1.5 + 2 ) = 5.5 Ω .

-----------------------------------------------------------------------------------------------------

Equivalent resistance between A and C :-

Resistors R

_{6 }and R_{8}are redundant to get equivalent resistance between A and C .Hence , they are removed in Step-1 as shown below

Now R

_{4 }, R_{5}and R_{7}are in series and equivalenet resistance of this series combination is 6 Ω .Hence in step-2 , this series combination is replaced by 6 Ω resistor .

Now resistor R

_{2}is in parallel with 6 Ω resistor,Equivalenet resistance of parallel combination is ( 2 × 6 ) / (2+6) = 1.5 Ω .

Hence, finally, resistance between A and C is ( 2 + 1.5 + 2 ) = 5.5 Ω .

--------------------------------------------------------------------------------------------------------

Equivalent resistance between A and D :-

Resistors R

_{6 }and R_{3}are redundant to get equivalent resistance between A and D .Hence , they are removed in Step-1 as shown below

R

_{2}and R_{5}are in series . Similarly R_{4}and R_{7}are in series .Series combination of R

_{2}and R_{5}, i.e., 4 Ω is in parallel to series combination of R_{4}and R_{7}which is 4 Ω .Hence two parallel 4 Ω resistors gives equivalenet resistance 2 Ω as shown in step-2 and step-3 .

Effective resistance between A and D is ( 2 + 2 + 2 ) Ω = 6 Ω

### Answered by Thiyagarajan K | 2nd Aug, 2021, 11:54: PM

## Application Videos

## Concept Videos

- Q. Find the current drawn from the battery by the network of 4 resistors shown in the diagram. Kindly Refer the file uploaded for diagram.
- please tell how to solve
- what is effective resisitance and how can we find it
- how to calculate the resistance if the resistors are inclined between parallel wires
- two lamps one rated 100w at 220 v and the other rated 200w at 220v are connected in 1.series 2. parallel to electirc main supplt of 220v. find the current drawn in each case
- Two lamps rated (100w, 220v) and (60w, 220v) are connected in parallel. which lamp consumes more energy and which one gives more brightness? Find the resistance of each lamp. ( Take supply voltage as 220 v).
- Find the equivalent resistance across wire A and B
- Is potential difference between different points of the circuit same or different
- Series combination proportional to its

### Kindly Sign up for a personalised experience

- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions

#### Sign Up

#### Verify mobile number

Enter the OTP sent to your number

Change