$1.$ In the circuit below, Bulb A has a resistance of $\backslash (10\backslash$Omega $\backslash ),$ Bulb B has a resistance of $\backslash (2\backslash$Omega $\backslash )$ and Bulb C has a resistance of $\backslash (3\backslash$Omega $\backslash ).$ The Battery voltage is $5$ V $.$

a$)$ What is the current through bulb A$?$

b$)$ What is the potential difference across bulb C $?$

$2.$ As a member of the safety group in the scientific program for the proposed space shuttle replacement vehicle, you have been asked to evaluate an electronics design change. In order to improve the reliability of a circuit to be used in the next shuttle flight, the experimental design team has suggested adding a $6$ V battery to the circuit shown below. The equivalent resistance of the devices in the proposed circuit design are also shown on the circuit diagram. You are worried about the device with the $\backslash (100\backslash$Omega $\backslash )$ resistance, which is rated at $25-$Watts $($which means it will fail if the power passing through it exceeds $25$ Watts$).$