To determine which circuits correctly show Ohm's Law, we need to ensure that for each circuit, the voltage [tex]\( V \)[/tex], current [tex]\( I \)[/tex], and resistance [tex]\( R \)[/tex] satisfy the equation [tex]\( V = I \times R \)[/tex].
We are given the following data:
1. Circuit 1:
- [tex]\( V = 25 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- [tex]\( R = \text{unknown} \)[/tex]
2. Circuit 2:
- [tex]\( V = 56 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- [tex]\( R = 5 \)[/tex] ohms
3. Circuit 3:
- [tex]\( V = 18 \)[/tex] volts
- [tex]\( I = 7 \)[/tex] amps
- [tex]\( R = \text{unknown} \)[/tex]
4. Circuit 4:
- [tex]\( V = 20 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- [tex]\( R = \text{unknown} \)[/tex]
Let's go through each circuit step-by-step.
### Circuit 1:
- Given:
- [tex]\( V = 25 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- Calculate [tex]\( R \)[/tex]:
- [tex]\( R = \frac{V}{I} = \frac{25}{5} = 5 \)[/tex] ohms
Since [tex]\( V = I \times R \)[/tex] holds true with [tex]\( R = 5 \)[/tex] ohms, Circuit 1 correctly shows Ohm's law.
### Circuit 2:
- Given:
- [tex]\( V = 56 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- [tex]\( R = 5 \)[/tex] ohms
- Verify [tex]\( V = I \times R \)[/tex]:
- Check [tex]\( 56 = 5 \times 5 \)[/tex]
Since [tex]\( 56 \neq 25 \)[/tex], Circuit 2 does not correctly show Ohm's law.
### Circuit 3:
- Given:
- [tex]\( V = 18 \)[/tex] volts
- [tex]\( I = 7 \)[/tex] amps
- Calculate [tex]\( R \)[/tex]:
- [tex]\( R = \frac{V}{I} = \frac{18}{7} \approx 2.57 \)[/tex] ohms (not an integer)
Since [tex]\( R \)[/tex] is not an integer, Circuit 3 does not correctly show Ohm's law.
### Circuit 4:
- Given:
- [tex]\( V = 20 \)[/tex] volts
- [tex]\( I = 5 \)[/tex] amps
- Calculate [tex]\( R \)[/tex]:
- [tex]\( R = \frac{V}{I} = \frac{20}{5} = 4 \)[/tex] ohms
Since [tex]\( V = I \times R \)[/tex] holds true with [tex]\( R = 4 \)[/tex] ohms, Circuit 4 correctly shows Ohm's law.
### Summary:
Based on the analysis, Circuits 1 and 4 correctly show Ohm's law. Hence, the circuits that correctly demonstrate Ohm's law are:
[tex]\[ \text{Circuits 1 and 4} \][/tex]
