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The text in the image appears to be discussing the time constant (denoted as **τ**) of an RC (resistor-capacitor) circuit. The time constant **τ** is given by the equation:

\[
\tau = R \cdot C
\]

where **R** is the resistance and **C** is the capacitance. The text mentions that you can increase **τ** either by changing the resistance or the capacitance. In the experiment described, the resistance was varied to change **τ**, and the question asks if changing the capacitance instead would result in the same effect on the rate of current change.

### Answer:
Yes, changing the capacitance will affect the time constant **τ** in the same way as changing the resistance, because **τ** is directly proportional to both resistance **R** and capacitance **C**. Increasing either **R** or **C** will increase **τ**, slowing the rate at which the current changes in the circuit. Conversely, decreasing either **R** or **C** will decrease **τ**, speeding up the rate of change of the current.

The rate of current change in an RC circuit is governed by the time constant. A larger **τ** means the circuit will take longer to charge or discharge, resulting in a slower change in current. Whether you adjust **R** or **C**, as long as **τ** changes, the effect on the rate of current change will be comparable.

### Would you like more detailed explanations or clarifications?

Here are five related questions to deepen your understanding:

1. How does changing both resistance **R** and capacitance **C** together affect the time constant **τ**?
2. What happens to the voltage across the capacitor if **τ** is increased by increasing either **R** or **C**?
3. How does the time constant **τ** affect the charging and discharging curves of the capacitor?
4. In practical applications, what considerations would guide whether to change **R** or **C** to adjust **τ**?
5. Can you calculate the exact change in **τ** if **C** is doubled and **R** remains constant?

### Tip:
In an RC circuit, the time constant **τ** also determines how long it takes for the voltage across the capacitor to reach approximately 63% of its maximum value during charging. After 5τ, the capacitor is nearly fully charged (over 99%).

Would you get the same change in the rate of current if we had changed the capacitance instead of changing the resistance?

Explore how changing capacitance affects the time constant (τ) in RC circuits. This problem involves understanding the relationship τ = R × C, explaining how variations in resistance and capacitance impact the rate of current change.

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