Equivalent resistance for resistors in series:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{1}}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{2}}}{\mathbf{+}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}{{\mathbf{R}}}_{{\mathbf{n}}}}$

Equivalent resistance for 2 resistors in parallel:

$\overline{){{\mathbf{R}}}_{{\mathbf{eq}}}{\mathbf{=}}\frac{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}{{\mathbf{R}}_{\mathbf{1}}\mathbf{+}{\mathbf{R}}_{\mathbf{2}}}}$

Current:

$\overline{){\mathbf{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

Power:

$\overline{){\mathbf{P}}{\mathbf{=}}{{\mathbf{i}}}^{{\mathbf{2}}}{\mathbf{R}}}$

**Part A.**

Equivalent resistance, R_{eq} = R_{1} + R_{2} + R_{1}

R_{eq} = 2R_{1} + R_{2}

Total voltage:

V = ε + ε = 2ε

Since the connection is in series, the current through all the components of circuit A is the same.

You are given two circuits with two batteries of emf ε and internal resistance R_{1} each. Circuit A has the batteries connected in series with a resistor of resistance R_{2}, and circuit B has the batteries connected in parallel to n equivalent resistor.

Part A. What is the current through the resistor of resistance R_{2} in circuit A?

Part B. Calculate the current I_{B} through the resistor of resistance R_{2} for circuit B?

Part C. What is the power dissipated by the resistor resistance R_{2} for circuit A, given the ε = 10 V, R_{1} = 300 ohms, and R_{2} = 5000 ohms?

Part D. For what ratio of R_{1} and R_{2} would power dissipated by the resistor of resistance R_{2} be the same for circuit A and circuit B?

Part E. Under which of the following conditions would power dissipated by the resistance R_{2} in circuit A be bigger than that of circuit B?

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