10.6 Household wiring and electrical safety  (Page 6/11)

The rather simple circuit shown below is known as a voltage divider. The symbol consisting of three horizontal lines is represents “ground” and can be defined as the point where the potential is zero. The voltage divider is widely used in circuits and a single voltage source can be used to provide reduced voltage to a load resistor as shown in the second part of the figure. (a) What is the output voltage $V_{\text{out}}$ of circuit (a) in terms of $R_1,R_2,\text{and}{V}_{\text{in}}?$ (b) What is the output voltage $V_{\text{out}}$ of circuit (b) in terms of $R_1,R_2,R_L,\text{and}{V}_{\text{in}}?$

Three $300\text{-}\text{Ω}$ resistors are connect in series with an AAA battery with a rating of 3 AmpHours. (a) How long can the battery supply the resistors with power? (b) If the resistors are connected in parallel, how long can the battery last?

Consider a circuit that consists of a real battery with an emf $\epsilon$ and an internal resistance of r connected to a variable resistor R . (a) In order for the terminal voltage of the battery to be equal to the emf of the battery, what should the resistance of the variable resistor be adjusted to? (b) In order to get the maximum current from the battery, what should the resistance variable resistor be adjusted to? (c) In order for the maximum power output of the battery to be reached, what should the resistance of the variable resistor be set to?

Consider the circuit shown below. What is the energy stored in each capacitor after the switch has been closed for a very long time?

Consider a circuit consisting of a battery with an emf $\epsilon$ and an internal resistance of r connected in series with a resistor R and a capacitor C . Show that the total energy supplied by the battery while charging the battery is equal to ${\epsilon }^{2}C$ .

Consider the circuit shown below. The terminal voltages of the batteries are shown. (a) Find the equivalent resistance of the circuit and the current out of the battery. (b) Find the current through each resistor. (c) Find the potential drop across each resistor. (d) Find the power dissipated by each resistor. (e) Find the total power supplied by the batteries.

Consider the circuit shown below. (a) What is the terminal voltage of the battery? (b) What is the potential drop across resistor $R_2$ ?

Consider the circuit shown below. (a)Determine the equivalent resistance and the current from the battery with switch $S_1$ open. (b) Determine the equivalent resistance and the current from the battery with switch $S_1$ closed.

Two resistors, one having a resistance of $145\text{Ω}$ , are connected in parallel to produce a total resistance of $150\text{Ω}$ . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Two resistors, one having a resistance of $900\text{k}\text{Ω},$ are connected in series to produce a total resistance of $0.500\text{M}\text{Ω}$ . (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?