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T=277+4s The temperature in kelvin, T, of a resistor in a circuit s seconds after connecting a battery is given by the equation. For how many seconds does the battery need to be connected for the temperature to increase by 1 kelvin? Choose 1 answer: (A) 0.25 (B) 4 (C) 69 (D) 277

T=277+4sT=277+4s\newlineThe temperature in kelvin, TT, of a resistor in a circuit ss seconds after connecting a battery is given by the equation. For how many seconds does the battery need to be connected for the temperature to increase by 11 kelvin?\newlineChoose 11 answer:\newline(A) 0.250.25\newline(B) 44\newline(C) 6969\newline(D) 277277

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Full solution

Q. T=277+4sT=277+4s\newlineThe temperature in kelvin, TT, of a resistor in a circuit ss seconds after connecting a battery is given by the equation. For how many seconds does the battery need to be connected for the temperature to increase by 11 kelvin?\newlineChoose 11 answer:\newline(A) 0.250.25\newline(B) 44\newline(C) 6969\newline(D) 277277
  1. Given Equation: We are given the equation T=277+4sT = 277 + 4s, where TT is the temperature in kelvin and ss is the time in seconds after connecting a battery. We want to find the value of ss that corresponds to an increase of 11 kelvin in temperature.
  2. Denote Initial Temperature: Let's denote the initial temperature as TinitialT_{\text{initial}}. After an increase of 11 kelvin, the new temperature will be Tinitial+1T_{\text{initial}} + 1. We can set up the equation Tinitial+1=277+4sT_{\text{initial}} + 1 = 277 + 4s to find the value of ss that corresponds to this increase.
  3. Set Up Equation: Since we are looking for the increase in temperature, we don't actually need to know the initial temperature. We can simply use the fact that the increase is 11 kelvin. So, we can write the equation as T+1=T+4sT + 1 = T + 4s, where TT is the initial temperature and T+1T + 1 is the temperature after the increase.
  4. Subtract and Simplify: Subtracting TT from both sides of the equation T+1=T+4sT + 1 = T + 4s gives us 1=4s1 = 4s.
  5. Find the Value: To find the value of ss, we divide both sides of the equation 1=4s1 = 4s by 44, which gives us s=14s = \frac{1}{4} or s=0.25s = 0.25 seconds.

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