The given question involves understanding the body effect in MOSFETs and its impact on threshold voltage.

Concepts to Understand:

• Body Effect in MOSFET: The body effect occurs because the potential difference between the body (substrate) and the source affects the threshold voltage \(V_{\text{th}}\) of a MOSFET.
• Threshold Voltage \(V_{\text{th}}\): It is the minimum gate-to-source voltage required to create a conducting path between the source and the drain.
• The body effect is quantified by the relationship: \(V_{\text{th}} = V_{\text{th0}} + \gamma (\sqrt{\phi_{\text{B0}} + V_{\text{SB}}} - \sqrt{\phi_{\text{B0}}})\), where:
  • \(V_{\text{th0}}\) is the threshold voltage at zero body bias.
  • \(\gamma\) is the body effect coefficient.
  • \(\phi_{\text{B0}}\) is the surface potential at zero body bias.
  • \(V_{\text{SB}}\) is the source-body voltage.

Analysis of the Given Statements:

1. Assertion (A): "The body effect in MOSFET causes the threshold voltage \(V_{\text{th}}\) to increase as source-body voltage \(V_{\text{SB}}\) increases." 
   This statement is correct because as the source-body voltage \(V_{\text{SB}}\) increases, the threshold voltage \(V_{\text{th}}\) indeed increases according to the body effect relationship.
2. Reason (R): "Increasing \(V_{\text{SB}}\) raises the surface potential and therefore reduces the barrier for inversion." 
   This statement is incorrect because increasing \(V_{\text{SB}}\) actually results in an increase in the threshold voltage, which indicates a higher barrier for inversion, not a reduction.

Conclusion:

Thus, while the assertion (A) is correct, the reason (R) incorrectly explains the effect of increasing \(V_{\text{SB}}\) on the surface potential and threshold voltage. Therefore, the most appropriate answer is:

(A) is correct but (R) is not correct.