The problem shown on the screen is about finding the equivalent resistance of a parallel circuit with three resistors.

Given Data:

• $V_{\text{battery}} = 12V$ (not needed for resistance calculation)
• $R_1 = 50\Omega$
• $R_2 = 100\Omega$
• $R_3 = 100\Omega$

Formula for Equivalent Resistance in Parallel:

$\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Substituting the Given Values:

$\frac{1}{R_{\text{eq}}} = \frac{1}{50} + \frac{1}{100} + \frac{1}{100}$

Converting to a Common Denominator:

$\frac{1}{R_{\text{eq}}} = \frac{2}{100} + \frac{1}{100} + \frac{1}{100}$

$\frac{1}{R_{\text{eq}}} = \frac{4}{100}$

$R_{\text{eq}} = \frac{100}{4} = 25\Omega$

Final Answer:

$R_{\text{eq}} = 25\Omega$

Let me know if you want a step-by-step explanation! Here are some related questions:

1. How do you calculate total resistance in a series circuit?
2. What happens to the total resistance if more resistors are added in parallel?
3. How do you calculate the current flowing through each resistor in this circuit?
4. What is the voltage drop across each resistor in a parallel circuit?
5. How does power consumption change in a parallel circuit?

Tip: In a parallel circuit, the total resistance is always less than the smallest resistor in the network!