For an RC circuit with time constant tau = R * C, which action will increase the time constant without altering topology?

Introduction:The time constant tau = R * C determines how fast an RC circuit responds to changes. This question probes which modification increases tau without changing the basic series or parallel structure.

Given Data / Assumptions:

• Time constant tau equals R multiplied by C.
• We can add components in parallel to existing R or C blocks.
• Source characteristics do not alter component values.

Concept / Approach:To increase tau, either effective R must increase or effective C must increase. Adding a capacitor in parallel increases total capacitance because parallel capacitances add directly: C_total = C1 + C2 + ... .

Step-by-Step Solution:1) Start from tau = R * C.2) Identify how parallel addition affects components.3) Parallel capacitors raise C_total, thus raising tau.4) Parallel resistors lower R_total, which would reduce tau.

Verification / Alternative check:If C doubles while R stays the same, tau doubles. This matches both qualitative reasoning and quantitative calculation.

Why Other Options Are Wrong:Adding a resistor in parallel: reduces R_total, decreasing tau.Increasing input amplitude: affects signal level, not R or C values, so tau is unchanged.Exchanging component order: in a series RC the order does not change tau.Decreasing source frequency: changes reactance seen in AC analysis, but tau as a component property R * C does not change.

Common Pitfalls:Confusing frequency response with time constant, or assuming larger signal amplitude slows the response. Only changing R or C changes tau.

Final Answer:adding a capacitor in parallel with the circuit capacitance