What is the time constant for a resistor of 5 mega ohms placed in series with a capacitor of 0.005 micro farads?

The time constant for an RC (resistor-capacitor) circuit, denoted by the symbol τ (tau), is calculated using the formula:

τ = R × C

where R is the resistance in ohms and C is the capacitance in farads. In this case, you have a resistor with a value of 5 mega ohms, which is equivalent to 5,000,000 ohms, and a capacitor with a capacitance of 0.005 micro farads, equal to 0.005 × 10^-6 farads (or 5 × 10^-9 farads).

Plugging these values into the formula gives:

τ = R × C = (5,000,000 ohms) × (5 × 10^-9 farads)

Calculating this yields:

τ = 5,000,000 × 5 × 10^-9 = 0.025 seconds

This calculation leads directly to the conclusion that the time constant is 0.025 seconds, making this the correct answer. The time constant represents the amount of time it takes for the capacitor to charge to approximately 63.2% of the maximum voltage across it when connected to a voltage source or to discharge