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The 5 Ohm resistor will have more current passing through it than the 10 ohm resistor. Since the resistors are in parallel the Voltage across each resistor is the same.

Power or the amount of heat in terms of the question can be derived from Power = Voltage * Current.

Ohm's law tells us that the current flowing through a resistor is equal to the Voltage across the resistor divided by the resistance. The formula for power is then the Voltage * Voltage / Resistance.

Since V^2 / 10 is smaller than V^2 / 5 we know that the 5 ohm resistor will always have more power dissipated than the 10 ohm resistor.

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