A given wire has a resistance of 32 ohms. If its length is 872 m., how much length must be
cut-off from the wire in order to reduce its resistance to 13.4 ohms?
We know that
Resistance
R=ρlAR=\frac{\rho l}{A}R=Aρl
R1=ρl1AR_1=\frac{\rho l_1}{A}R1=Aρl1
Case (2)
R2=ρl2AR_2=\frac{\rho l_2}{A}R2=Aρl2
R1R2=l1l2\frac{R_1}{R_2}=\frac{l_1}{l_2}R2R1=l2l1
l2=R2R1l1l_2=\frac{R_2}{R_1}l_1l2=R1R2l1
l2=13.432×872=365.15ml_2=\frac{13.4}{32}\times872=365.15ml2=3213.4×872=365.15m
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