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The blower motor resistor for the cabin fan in a Volvo 850/V70 is so big that it is not even part of the motor. It has its own mounting. Here is a picture:

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Why does the blower require such a large resistor? I have much larger fans in my house that have no such resistor.

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The resistor is used for voltage reduction to the DC motor in your car fan. The power dissipated in the resistor can be calculated from \$ P = \frac {V^2}{R} \$ or \$ P = I^2 R \$. The resistor needs to be able to radiate this heat away without getting so hot that it melts nearby plastic components or setting itself on fire - hence the size.

The fans in your house are AC and so a capacitor can be used to reduce the voltage without any power being dissipated. A capacitor has an impedance (the resistance to AC) given by \$ Z = \frac {1}{\omega C} = \frac {1}{2 \Pi f C}\$. The current through the capacitor is 90° out of phase with the voltage so the power dissipated is zero.

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The V70 is 25+ year-old design so it uses fairly primitive methods. A series resistor (switched for selection) is an acceptable way if controlling speed of a brushed DC motor driving a blower load. The worst case dissipation of such a resistor is half the motor full power consumption, but the designers also have to consider the possibility of the motor stalling due to worn-out bearings or debris sucked into the fan (or possibly critters).

You will note the one-time thermal cutoff (fuse) mounted at one end to deal with over temperature.

The large physical size results from the required worst-case power dissipation and the requirement that the part should not run (say) red hot for safety and reliability reasons. The resistances are relatively low and the voltage does not much exceed 12V.

More modern cars may use a large MOSFET and pulse-width modulation to control the blower speed. AC fans such as ceiling fans use different methods to control speed.

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If that was only one effective resistor it would only need two wires.

It has several connections matched to the number of speeds available for the heater, 3 or possibly 4, which is why it is so large also due to the current it has to pass.

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