Three sample-state rows show that the held value follows the input source exactly. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two input volts capture two held volts

With the switch closed, a 2 volt input is the source of the same 2 volt held output.

Vheld=Vin=2 VV_{\text{held}}=V_{\text{in}}=2\ \text{V}
Two-volt sample rowThe closed switch makes held voltage equal input voltage.closed2 FV2 VV2 V+-2 V+-2 V+-2 Vsample

Four input volts capture four held volts

Only the source input changes. The capacitance stays 2 farads, and the held output becomes 4 volts.

Vheld=Vin=4 VV_{\text{held}}=V_{\text{in}}=4\ \text{V}
Four-volt sample rowThe same sample rule is applied to the middle input.closed2 FV4 VV4 V+-4 V+-4 V+-4 Vsample

Six input volts capture six held volts

The third row confirms the proportional rule: sample state copies the 6 volt input into the held node.

Vheld=Vin=6 VV_{\text{held}}=V_{\text{in}}=6\ \text{V}
Six-volt sample rowThe output meter and held marker agree with the input marker.closed2 FV6 VV6 V+-6 V+-6 V+-6 Vsample