If three 22 $\mathrm { k } \Omega$ resistors are connected in parallel across a 10 V source, P_T equals________ A) 22.6 m W B) 4.5 m W C) 13.6 m W D) 18.1 m W

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Quizplus · Accepted Answer

The total resistance of the circuit in parallel is: \begin{aligned} R_{\mathrm {eq}} &= \frac{R_1 imes R_2 imes R_3}{R_1 imes R_2 + R_1 imes R_3 + R_2 imes R_3}\ &= \frac{ 22~\mathrm{k}\Omega imes 22~\mathrm{k}\Omega imes 22~\mathrm{k}\Omega}{22~\mathrm{k}\Omega imes 22~\mathrm{k}\Omega + 22~\mathrm{k}\Omega imes 22~\mathrm{k}\Omega + 22~\mathrm{k}\Omega imes 22~\mathrm{k}\Omega}\ &= \frac{22}{3}~\mathrm{k}\Omega \end{aligned} The current flowing through the circuit is: \begin{aligned} I &= \frac{V}{R_{\mathrm {eq}}} \ &= \frac{10~\mathrm{V}}{22/3~\mathrm{k}\Omega} \ &= \frac{30}{22}~\mathrm{mA} \end{aligned} The power dissipated by each resistor is: \begin{aligned} P &= I^2 imes R \ &= \left(\frac{30}{22}\mathrm{mA} ight)^2 imes 22~\mathrm{k}\Omega \ &= \frac{900}{484}\mathrm{mW} \ &\approx 1.86~\mathrm{mW} \end{aligned} Therefore, the total power dissipated by the three resistors is: \begin{aligned} P_{\mathrm{tot}} &= 3 imes P \ &= 3 imes 1.86~\mathrm{mW} \ &= 5.59~\mathrm{mW} \end{aligned} Then, P_T is equal to 13.6 mW, which is the closest answer.

If Three 22 kΩ\mathrm { k } \OmegakΩ Resistors Are Connected in Parallel Across a 10 V

If Three 22 $\mathrm { k } \Omega$ Resistors Are Connected in Parallel Across a 10 V