Time Constant of R-C Circuit:
The time constant (T) of an RC circuit is a measure of how quickly the circuit charges or discharges. It is defined as the time it takes for the voltage across the capacitor (or the current through the resistor) to reach approximately 63.2% of its final value. The time constant is given by the equation T = RC, where R is the resistance and C is the capacitance.

Given:
Time constant (T) = 2 sec
Supply voltage (V) = 10 V
Time (t) = 1 sec
e^(-0.5) = 0.61

Calculating the Voltage across the Resistor:
To find the voltage across the resistor at t = 1 sec, we need to calculate the charge on the capacitor at that time.

1. Calculate the Capacitance:
From the equation T = RC, we can rearrange it to find the capacitance:
C = T/R
Given T = 2 sec, but the resistance value is not provided. Therefore, we cannot directly calculate the capacitance.

2. Calculate the Resistor:
Since we don't have the resistance value, we need to find it using the time constant equation:
T = RC
R = T/C
Given T = 2 sec, but the capacitance value is not provided. Therefore, we cannot directly calculate the resistance.

3. Calculate the Voltage across the Capacitor:
The voltage across the capacitor at time t is given by the formula:
Vc(t) = V(1 - e^(-t/T))
where Vc(t) is the voltage across the capacitor at time t, V is the supply voltage, and T is the time constant.

Given: V = 10 V, t = 1 sec, T = 2 sec
Vc(1) = 10(1 - e^(-1/2))
Vc(1) = 10(1 - 0.61)
Vc(1) = 10(0.39)
Vc(1) = 3.9 V

Answer:
The voltage across the resistor at t = 1 sec is 3.9 V.