**Problem 3:** For what emf \( \mathcal{E} \) does the 200Ω resistor in Fig. 3 dissipate no power? Should the emf be oriented with its positive terminal at the top or at the bottom? a) If the 200Ω resistor dissipates no power, what does this mean for the distribution of the currents in the circuit? In other words, how are the currents through the different resistors related in this case? b) Choose any two different closed loops in the circuit and write down Kirchhoff's loop law for these loops. It must be possible to solve these two equations for the current and the emf \( \mathcal{E} \). **Figure 3: Circuit Diagram for Problem 3** - The circuit consists of a 50V battery oriented with the positive terminal at the top. - There are three resistors: 100Ω and 300Ω in series, with a 200Ω resistor in parallel with the 100Ω resistor. - An unknown emf \( \mathcal{E} \) is in series with the 300Ω resistor. This setup requires solving for the emf \( \mathcal{E} \) and understanding current distribution using principles like Kirchhoff's loop law.

Problem 3: For what emf \( \mathcal{E} \) does the 200Ω resistor in Fig. 3 dissipate no power? Should the emf be oriented with its positive terminal at the top or at the bottom? a) If the 200Ω resistor dissipates no power, what does this mean for the distribution of the currents in the circuit? In other words, how are the currents through the different resistors related in this case? b) Choose any two different closed loops in the circuit and write down Kirchhoff's loop law for these loops. It must be possible to solve these two equations for the current and the emf \( \mathcal{E} \). Figure 3: Circuit Diagram for Problem 3 - The circuit consists of a 50V battery oriented with the positive terminal at the top. - There are three resistors: 100Ω and 300Ω in series, with a 200Ω resistor in parallel with the 100Ω resistor. - An unknown emf \( \mathcal{E} \) is in series with the 300Ω resistor. This setup requires solving for the emf \( \mathcal{E} \) and understanding current distribution using principles like Kirchhoff's loop law.