For two conduction layers in series, which expression correctly gives the total resistance?

For two conduction layers in series, which expression correctly gives the total resistance?

• A. R_total = (L1+L2)/(k A)
• B. R_total = L1/(k1 A1) + L2/(k2 A2)
• C. R_total = kA/(L1+L2)
• D. R_total = L1/(k1 A1) * L2/(k2 A2)

Answer: (B)

When layers conduct in series, the total resistance is the sum of the individual resistances. Each layer’s resistance is determined by its thickness, conductivity, and cross-sectional area: R = L/(kA). So for two layers in series, the overall resistance is L1/(k1A1) + L2/(k2A2). This captures the possibility that the materials or cross-sections differ between layers. If both layers shared the same k and A, it would simplify to (L1+L2)/(kA), but that’s a special case of the general add-in-series rule. The other forms would not represent the correct series combination: they either assume uniform properties across layers, or they mix in reciprocal or product relationships that don’t reflect how resistances add in series.

When layers conduct in series, the total resistance is the sum of the individual resistances. Each layer’s resistance is determined by its thickness, conductivity, and cross-sectional area: R = L/(kA). So for two layers in series, the overall resistance is L1/(k1A1) + L2/(k2A2). This captures the possibility that the materials or cross-sections differ between layers. If both layers shared the same k and A, it would simplify to (L1+L2)/(kA), but that’s a special case of the general add-in-series rule. The other forms would not represent the correct series combination: they either assume uniform properties across layers, or they mix in reciprocal or product relationships that don’t reflect how resistances add in series.