Два последовательно соединенных проводника, сопротивления которых равны соответственно $R_1=5$ Ом и $R_2=10$ Ом, подключены к источнику тока с напряжением $90$ В. Определите мощность, выделяемую на проводнике с сопротивлением $R_2$ . (Ответ получите в Дж и округлите до целых)

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Grade 8

Identify independent and dependent variables

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Q. Два последовательно соединенных проводника, сопротивления которых равны соответственно

R_1=5

Ом и

R_2=10

Ом, подключены к источнику тока с напряжением

90

В. Определите мощность, выделяемую на проводнике с сопротивлением

R_2

. (Ответ получите в Дж и округлите до целых)

Calculate Total Resistance: question_prompt: How much power is dissipated in the second resistor with a resistance of $R_2=10\,\Omega$ when connected in series with another resistor $R_1=5\,\Omega$ to a $90\,V$ power source?
Find Total Current: Step $1$ : Calculate the total resistance in the circuit since the resistors are connected in series. $\newline$ Total resistance $R_{\text{total}}$ = $R_1 + R_2$ $\newline$ $R_{\text{total}}$ = $5 \Omega + 10 \Omega$ $\newline$ $R_{\text{total}}$ = $15 \Omega$
Calculate Voltage Drop: Step $2$ : Use Ohm's Law to find the total current ( $I$ ) flowing through the circuit. $\newline$ Ohm's Law: $V = I \times R_{\text{total}}$ $\newline$ $90\,\text{V} = I \times 15\,\Omega$ $\newline$ $I = \frac{90\,\text{V}}{15\,\Omega}$ $\newline$ $I = 6\,\text{A}$
Calculate Power Dissipated: Step $3$ : Calculate the voltage drop $V_2$ across the second resistor $R_2$ using Ohm's Law. $V_2 = I \times R_2$ $V_2 = 6 \, \text{A} \times 10 \, \Omega$ $V_2 = 60 \, \text{V}$
Convert Power to Joules: Step $4$ : Calculate the power $P_2$ dissipated in the second resistor using the formula $P = \frac{V^2}{R}$ . $P_2 = \frac{V_2^2}{R_2}$ $P_2 = \frac{60^2 \text{ V}}{10 \Omega}$ $P_2 = \frac{3600 \text{ V}^2}{10 \Omega}$ $P_2 = 360 \text{ W}$
Convert Power to Joules: Step $4$ : Calculate the power $P_2$ dissipated in the second resistor using the formula $P = \frac{V^2}{R}$ . $P_2 = \frac{V_2^2}{R_2}$ $P_2 = \frac{60^2 \text{ V}}{10 \Omega}$ $P_2 = \frac{3600 \text{ V}^2}{10 \Omega}$ $P_2 = 360 \text{ W}$ Step $5$ : Convert the power from watts to joules since $1 \text{ watt}$ is equal to $1 \text{ joule}$ per second and we are not given a time period, we assume the power is the energy per second. $P_2$ in joules = $360 \text{ J}$ (since $P = \frac{V^2}{R}$ $0$ and we assume $P = \frac{V^2}{R}$ $1$ second)