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To increase the current stability of a common collector (CC) amplifier, increasing the emitter resistance while decreasing the base resistance is an effective strategy.

In a CC amplifier, the emitter resistor plays a crucial role in thermal stability and bias stability. By increasing the emitter resistance, you enhance the negative feedback in the circuit, which helps stabilize the current against variations in temperature and transistor characteristics. This means that if the transistor's characteristics change (perhaps due to temperature fluctuations), the additional emitter resistance helps to mitigate these changes by reducing the gain of the circuit, thus allowing for a more stable output current.

On the other hand, decreasing the base resistance allows for a greater base current, which can ensure that the transistor remains in the active region without driving it into saturation. This combination of increased emitter resistance and controlled base resistance provides a balance that promotes current stability, preventing issues such as thermal runaway and ensuring consistent performance across varying conditions.

The other choices do not achieve the same beneficial effects for current stability.