For the circuit shown below;

• Write a KCL equation for Node A, Node B, Node C and Node D.
• Write a KVL equation for Loop 1, Loop 2 and Loop 3.

A simple circuit to charge a 12V battery is shown below. A fixed DC voltage source is set to the required maximum charging voltage, usually 14.5V. The resistor R1 is used to limit the initial charging current when the battery is discharged.

(i)  Design a battery charger circuit to charge a 12V battery from a 14.5V fixed DC voltage source. The charger should have two maximum current settings selected by a 2 position switch. The high setting should provide a maximum charge current of 1A and the low setting should provide a maximum current of 300mA. Assume a fully discharged 12V battery has a voltage of 10.8V across its terminals. Include a voltmeter and ammeter in your circuit design to allow the battery voltage and current to be monitored while charging. Draw the schematic of the battery charger showing all component values.
 
(ii) For each current setting redraw the circuit showing all voltages and currents when charging a fully discharged battery. Calculate the power dissipated in the resistor, the power delivered to the battery and the power provided by the DC voltage source. How efficient is the battery charger for each setting. 
 
Resistors only come in a limited range of 'preferred' values so it is not often possible to buy the value you want "off the shelf". Assume you have the resistors shown in table one available.

(i)  Suggest, showing all calculations, how you could build the circuit using only these available resistors.

(ii) Using these new resistor values recalculate the maximum charge current for each setting.