If A and B are identical bulbs,which bulb glo | vedclass

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(A) The brightness of a bulb depends on the power dissipated,which is given by $P = I^2 R$. Since the bulbs are identical,their resistance $R$ is the

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$A$

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(A) The brightness of a bulb depends on the power dissipated,which is given by $P = I^2 R$. Since the bulbs are identical,their resistance $R$ is the same. Therefore,the bulb with the higher current $I$ will glow brighter.In the circuit,bulb $A$ is in series with an inductor of $100 \ mH$,and bulb $B$ is in series with a capacitor of $10 \ pF$. The current in each branch is determined by the impedance: $I_A = V / Z_A$ and $I_B = V / Z_B$,where $Z_A = \sqrt{R^2 + X_L^2}$ and $Z_B = \sqrt{R^2 + X_C^2}$.For a typical $AC$ source frequency,the capacitive reactance $X_C = 1 / (\omega C)$ is much larger than the inductive reactance $X_L = \omega L$. However,in this specific circuit,the capacitor has a very small capacitance $(10 \ pF)$,making $X_C$ extremely large compared to $X_L$. Consequently,the impedance $Z_B$ is much larger than $Z_A$.Since $Z_A < Z_B$,the current $I_A$ is greater than $I_B$. Thus,bulb $A$ glows brighter.

If $A$ and $B$ are identical bulbs,which bulb glows brighter?

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