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CBSE Class 10 Science Exam 2014 Term 1 Paper

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Question : 16
Total: 36
Show four different ways in which four resistors of r ohm each may be connected in a circuit. In which case is the equivalent resistance of the combination.
(i) maximum;
(ii) minimum ?
Solution:  
(a)
Resultant resistance, R=r+r+r+r
R=4r
(b)
‌
1
R
‌=‌
1
r
+‌
1
r
+‌
1
r
+‌
1
r
=‌
4
r

‌=‌
4
r

R‌=‌
r
4
(c)
Resistance (AB)=R1=r+r=2r
Resistance (PQ)=R2=r+r=2r
Resultant resistance, R= ?
‌
1
R
=‌
1
R1
+‌
1
R2
=‌
1
2r
+‌
1
2r
=‌
1+1
2r
=‌
2
2r
=‌
1
r

R=r
(d)
Resistance (PQ)=R1=r+r+r=3r
Resistance (AB)=R2=r
Resultant Resistance, R= ?
‌
1
R
=‌
1
R1
+‌
1
R2
=‌
1
3r
+‌
1
r
=‌
1+3
3r
=‌
4
3r

R=‌
3r
4

(i) Maximum resistance is in case (1) where all the resistors are combined in series.
(ii) Minimum resistance is in case (2) where all the resistors are combined in parallel combination.
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