when two resistors are connected in series the equivalent resistance is 25ohm when they are connected in in parallel research resistance is 6ohm . find the value of two resistence
Answers
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Explanation:
The total resistance of resistors in series is equal to the sum of their individual resistances. That is, R
total
=R
1
+R
2
+R
3
.
The total resistance will always be less than the value of the smallest resistance That is,
R
total
1
=
R
1
1
+
R
2
1
+
R
3
1
thatis,R=R
total
−1
.
In this case, the total resistance of the resistors connected in series is given as R
1
+R
2
=45 - eqn 1
The total resistance of the resistors connected in parallel is given as
R
1
1
+
R
2
1
=
10
1
thatis,
R
1
1
+
R
2
1
=0.1 - eqn 2
Putting the value of R
1
+R
2
in eqn 2, we get, R
1
R
2
=10×45=450ohms.
Now, From the identity, (R
1
−R
2
)
2
=(R
1
+R
2
)
2
−4R
1
R
2
,weget,R
1
−R
2
=15ohms - eqn 3.
Adding eqn 2 and eqn 3,
2R
1
=60ohmsThatis,R
1
=30ohms.
Substituting this value in eqn 3, we get, R
2
=(30−15)=15ohms.
Hence, the values of the resistors are 30 ohms and 15 ohms.