Final answer:
A bleeder resistor in a firm voltage divider must have a resistance much greater than the load to prevent altering the circuit's effective resistance and to allow for a safe discharge of capacitors.
Step-by-step explanation:
A firm voltage divider uses a bleeder resistor which is much greater than the resistance of the load. The reason the bleeder resistance needs to be significantly higher is to ensure that it does not alter the effective resistance of the entire circuit drastically. The voltmeter example provided illustrates this principle, as a voltmeter with high resistance compared to the device it measures does not appreciably affect the circuit (Figure 21.31(a)), while one with resistance comparable to the device alters the overall resistance and the voltage across the device (Figure 21.31(b)). In the case of the bleeder resistor, having a resistance much greater than the effective resistance of the rest of the circuit ensures that it will not significantly impact the operation of the circuit while the power is on. Moreover, a high resistance will dictate a longer time constant for discharging the capacitor, allowing it to slowly and safely bleed off the charge after the apparatus is turned off, thereby mitigating the shock hazard posed by the charged capacitor.