I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
To determine how long a 3Ah battery will last given the voltage drop and resistor value, we need to follow these steps: 1. **Calculate the current (I) using Ohm's Law**: \[ V = IR \] Where \( V \) is the voltage drop (30 mV = 0.03 V) and \( R \) is the resistance (2.5 ohms). \[ I = \frac{V}{R} = \frac{0.03 \text{ V}}{2.5 \text{ ohms}} = 0.012 \text{ A} \text{ or } 12 \text{ mA} \] 2. **Determine the battery life (T)**: The battery capacity is given as 3Ah. This means the battery can provide 3 amps for 1 hour, or 1 amp for 3 hours, etc. Using the current we calculated: \[ T = \frac{\text{Battery Capacity}}{I} = \frac{3 \text{ Ah}}{0.012 \text{ A}} \] \[ T = 250 \text{ hours} \] So, the battery will last **250 hours**.
Testing if the previous output matches the regex 250.{,10}hours: True
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
To determine how long a 3Ah battery will last, we need to calculate the current flowing through the resistor and then use that current to find the battery life. 1. **Calculate the current flowing through the resistor:** Using Ohm's Law, \( V = I \times R \): \[ I = \frac{V}{R} \] Given: - Voltage drop, \( V = 30 \text{ mV} = 0.03 \text{ V} \) - Resistance, \( R = 2.5 \text{ ohms} \) \[ I = \frac{0.03 \text{ V}}{2.5 \text{ ohms}} = 0.012 \text{ A} = 12 \text{ mA} \] 2. **Determine the battery life:** Battery capacity is given as 3Ah (Ampere-hours). To find how long the battery will last, we use the formula: \[ \text{Battery Life} = \frac{\text{Battery Capacity}}{\text{Current}} \] Given: - Battery capacity = 3Ah - Current = 12mA = 0.012A \[ \text{Battery Life} = \frac{3 \text{ Ah}}{0.012 \text{ A}} = 250 \text{ hours} \] So, the battery will last **250 hours**.
Testing if the previous output matches the regex 250.{,10}hours: True
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
First, let's determine the current flowing through the resistor using Ohm's Law: \[ V = I \times R \] Given: - \( V = 30 \text{ mV} = 0.03 \text{ V} \) - \( R = 2.5 \text{ ohms} \) Rearranging Ohm's Law to solve for current \( I \): \[ I = \frac{V}{R} = \frac{0.03 \text{ V}}{2.5 \text{ ohms}} = 0.012 \text{ A} \] Next, we calculate how long the battery will last. The battery capacity is given as 3Ah, which means it can supply 3 amps for 1 hour, or equivalently, 1 amp for 3 hours, etc. To find the time \( t \) the battery will last at the current \( I \): \[ t = \frac{\text{Battery Capacity}}{\text{Current}} = \frac{3 \text{ Ah}}{0.012 \text{ A}} = 250 \text{ hours} \] So, the battery will last: \[ 250 \text{ hours} \]
Testing if the previous output matches the regex 250.{,10}hours: True
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
To determine how long a 3Ah battery will last given the voltage drop over the resistor, follow these steps: 1. **Calculate the current (I) flowing through the resistor** using Ohm's Law: \[ V = IR \] Given: \[ V = 30 \text{ mV} = 0.03 \text{ V} \] \[ R = 2.5 \text{ ohms} \] \[ I = \frac{V}{R} = \frac{0.03 \text{ V}}{2.5 \text{ ohms}} = 0.012 \text{ A} = 12 \text{ mA} \] 2. **Determine the battery life** by dividing the battery capacity by the current: \[ \text{Battery Life} = \frac{\text{Capacity}}{\text{Current}} = \frac{3 \text{ Ah}}{0.012 \text{ A}} = 250 \text{ hours} \] So, the battery will last for: \[ \boxed{250 \text{ hours}} \]
Testing if the previous output matches the regex 250.{,10}hours: True
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
I measure a voltage drop of 30mv over a 2.5 ohm resistor. How long will a 3Ah battery last? Write your ansser 'XXX hours'
To determine how long a 3Ah (Ampere-hour) battery will last given a voltage drop of 30mV over a 2.5 ohm resistor, we need to follow these steps: 1. **Calculate the current (I) using Ohm's Law:** \[ I = \frac{V}{R} \] where \( V \) is the voltage drop (30mV or 0.03V) and \( R \) is the resistance (2.5 ohms). \[ I = \frac{0.03V}{2.5\Omega} = 0.012A \text{ (or 12mA)} \] 2. **Determine the battery life:** The battery's capacity is 3Ah (Ampere-hours), which means it can supply 3A for 1 hour, 1.5A for 2 hours, etc. To find how long it can supply 0.012A, we use the following formula: \[ \text{Battery life} = \frac{\text{Battery capacity}}{\text{Current}} \] Plugging in the values: \[ \text{Battery life} = \frac{3Ah}{0.012A} = 250 \text{ hours} \] So, the battery will last **250 hours**.
Testing if the previous output matches the regex 250.{,10}hours: True