Two wires having resistance of 6 Ω and 3 Ω are connected to same voltage. Ratio of heat dissipated at resistance is
Question
Two wires having resistance of 6 Ω and 3 Ω are connected to same voltage. Ratio of heat dissipated at resistance is
Solution
The heat dissipated in a resistor in an electrical circuit is given by the formula H = I^2R, where I is the current through the resistor and R is the resistance.
However, in this case, the two resistors are connected to the same voltage source. Therefore, the current through each resistor will be different, according to Ohm's law (V = IR), where V is the voltage, I is the current, and R is the resistance.
Let's denote the voltage as V. The current through the 6 Ω resistor will be V/6, and the current through the 3 Ω resistor will be V/3.
The heat dissipated in the 6 Ω resistor is H1 = (V/6)^2 * 6 = V^2/6. The heat dissipated in the 3 Ω resistor is H2 = (V/3)^2 * 3 = V^2/3.
Therefore, the ratio of the heat dissipated in the 6 Ω resistor to the heat dissipated in the 3 Ω resistor is H1/H2 = (V^2/6) / (V^2/3) = 1/2.
So, the ratio of heat dissipated at the 6 Ω resistor to the 3 Ω resistor is 1:2.
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