When two springs are connected in series a constant force is applied on one of the springs and total extension is sum of elongation of each spring When two springs are in series F = k1x1 and F = k2x2 so
x1+x2 = total deformation = F/k1 + F/k2 = F/k
k = (1/k1 +1/k2)^-1
When two springs are connected in parallel a constant force F is exerted on both of them and both spring are extended by same amount. System of two parallel spring will equal to single hookean spring
k = k1 + k2
Hence spring constant is different in case of parallel
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