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The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V=IR. Suppose that V is 1 amp/sec. Let t denote time in seconds. Answer the following questions. increasing at the rate of 3 volt/sec while I is decreasing at the rate of 5 dV = volt/sec (Simplify your answer.) dt dl b. What is the value of dt? dl dt OA. amp/sec (Simplify your answer.) c. What equation relates to O C. dR dt dR dV dt dt dR dt 1 dV dl +V- I dt dt dl dV =1=+W +VdT dt dl and dt? OB. O D. d. Find the rate at which R is changing when V = 40 volts and 1= 4 amp. Is R increasing or decreasing? R is changing at ohm/sec. (Simplify your answer.) Is R increasing or decreasing? dR dt dR dt 1 dV I'dt V dl dt I dt 1/dV 1 I F R www

The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V=IR. Suppose that V is 1 amp/sec. Let t denote time in seconds. Answer the following questions. increasing at the rate of 3 volt/sec while I is decreasing at the rate of 5 dV = volt/sec (Simplify your answer.) dt dl b. What is the value of dt? dl dt OA. amp/sec (Simplify your answer.) c. What equation relates to O C. dR dt dR dV dt dt dR dt 1 dV dl +V- I dt dt dl dV =1=+W +VdT dt dl and dt? OB. O D. d. Find the rate at which R is changing when V = 40 volts and 1= 4 amp. Is R increasing or decreasing? R is changing at ohm/sec. (Simplify your answer.) Is R increasing or decreasing? dR dt dR dt 1 dV I'dt V dl dt I dt 1/dV 1 I F R www

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The voltage \( V \) (volts), current \( I \) (amperes), and resistance \( R \) (ohms) of an electric circuit like the one shown here are related by the equation \( V = IR \). Suppose that \( V \) is increasing at the rate of 3 volts/sec while \( I \) is decreasing at the rate of \( \frac{1}{5} \) amp/sec. Let \( t \) denote time in seconds. Answer the following questions. a. \( \frac{dV}{dt} = \) [ ] volts/sec (Simplify your answer.) b. What is the value of \( \frac{dI}{dt}? \) \[ \frac{dI}{dt} = \] [ ] amp/sec (Simplify your answer.) c. What equation relates \( \frac{dR}{dt} \), \( \frac{dV}{dt} \), and \( \frac{dI}{dt}? \) - Option A: \( \frac{dR}{dt} = \frac{1}{I} \frac{dV}{dt} + V \frac{dI}{dt} \) - Option B: \( \frac{dR}{dt} = \frac{1}{I} \frac{dV}{dt} \) - Option C: \( \frac{dR}{dt} = -\frac{I}{I} \frac{dV}{dt} + \frac{dV}{dt} \) - Option D: \( \frac{dR}{dt} = \frac{1}{I} \left( \frac{dV}{dt} - V \frac{dI}{dt} \right) \) d. Find the rate at which \( R \) is changing when \( V = 40 \) volts and \( I = 4 \) amp. Is \( R \) increasing or decreasing? - \( R \) is changing at [ ] ohm/sec. (Simplify your answer.) - Is \( R \) increasing or decreasing? **Diagram Explanation:** The diagram is a simple electrical circuit consisting of a battery (represented by a long and short straight line) and a resistor (denoted by a zigzag line). The battery is labeled \( V \), the current flowing through the circuit is labeled \( I \), and the resistor
Transcribed Image Text:The voltage \( V \) (volts), current \( I \) (amperes), and resistance \( R \) (ohms) of an electric circuit like the one shown here are related by the equation \( V = IR \). Suppose that \( V \) is increasing at the rate of 3 volts/sec while \( I \) is decreasing at the rate of \( \frac{1}{5} \) amp/sec. Let \( t \) denote time in seconds. Answer the following questions. a. \( \frac{dV}{dt} = \) [ ] volts/sec (Simplify your answer.) b. What is the value of \( \frac{dI}{dt}? \) \[ \frac{dI}{dt} = \] [ ] amp/sec (Simplify your answer.) c. What equation relates \( \frac{dR}{dt} \), \( \frac{dV}{dt} \), and \( \frac{dI}{dt}? \) - Option A: \( \frac{dR}{dt} = \frac{1}{I} \frac{dV}{dt} + V \frac{dI}{dt} \) - Option B: \( \frac{dR}{dt} = \frac{1}{I} \frac{dV}{dt} \) - Option C: \( \frac{dR}{dt} = -\frac{I}{I} \frac{dV}{dt} + \frac{dV}{dt} \) - Option D: \( \frac{dR}{dt} = \frac{1}{I} \left( \frac{dV}{dt} - V \frac{dI}{dt} \right) \) d. Find the rate at which \( R \) is changing when \( V = 40 \) volts and \( I = 4 \) amp. Is \( R \) increasing or decreasing? - \( R \) is changing at [ ] ohm/sec. (Simplify your answer.) - Is \( R \) increasing or decreasing? **Diagram Explanation:** The diagram is a simple electrical circuit consisting of a battery (represented by a long and short straight line) and a resistor (denoted by a zigzag line). The battery is labeled \( V \), the current flowing through the circuit is labeled \( I \), and the resistor
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