Question

section 5 - 8 power in series circuits

1. five series resistors each handle 50 mw. what is the total power?
2. what is the total power in the circuit in figure 5 - 84? use the results of problem 43.
3. the following 1% w resistors are in series: 1.2 kω, 2.2 kω, 3.9 kω, and 5.6 kω. what is the maximum voltage that can be applied across the series resistors without exceeding a power - rating? which resistor will burn out first if excessive voltage is applied?
4. find rt in figure 5 - 85.

Explanation:

Step1: For question 46

In a series - circuit, the total power when components have the same power - handling capacity is the sum of the powers of individual components. Since there are 5 resistors each handling 50 mW, we use the formula $P_{total}=\sum_{i = 1}^{n}P_i$. Here, $n = 5$ and $P_i=50\ mW$.
$P_{total}=5\times50\ mW = 250\ mW$

Step2: For question 47

No information about Figure 5 - 84 is given, so we cannot solve this part.

Step3: For question 48

First, find the equivalent resistance of the series resistors $R_{eq}=1.2\ k\Omega+2.2\ k\Omega + 3.9\ k\Omega+5.6\ k\Omega=12.9\ k\Omega$. The power formula is $P=\frac{V^{2}}{R}$. We know the power rating of each resistor. Let's assume the power - rating of each resistor is the limiting factor. To find the maximum voltage $V$, we use the resistor with the lowest power - handling capability among them (assuming all have the same power rating for simplicity, say $P = 50\ mW$). Rearranging the power formula for $V$, we get $V=\sqrt{PR}$. Using $R = 12.9\ k\Omega$ and $P = 50\ mW=50\times10^{- 3}\ W$, $V=\sqrt{50\times10^{-3}\times12.9\times10^{3}}=\sqrt{645}\approx25.4\ V$. To find which resistor burns out first, the power formula $P = I^{2}R$. In a series circuit, the current is the same. The resistor with the highest resistance will have the highest power dissipated across it when the current is the same. So the $5.6\ k\Omega$ resistor will burn out first.

Step4: For question 49

No information about Figure 5 - 85 is given, so we cannot solve this part.

Answer:

1. $250\ mW$
2. Cannot be solved due to lack of information.
3. Maximum voltage: approximately $25.4\ V$, Resistor that burns out first: $5.6\ k\Omega$ resistor
4. Cannot be solved due to lack of information.