Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Two uncharged capacitors with [tex]C_1 = 25 \mu F[/tex] and [tex]C_2 = 75 \mu F[/tex] are connected in parallel to a battery with [tex]\varepsilon = 7.5 \text{ V}[/tex].

Calculate the numerical value of [tex]Q_1[/tex] in [tex]\mu C[/tex].

Sagot :

GinnyAnswer
To find the charge [tex]\( Q_1 \)[/tex] on capacitor [tex]\( C_1 \)[/tex], we start with the given values for the capacitors and the battery voltage. The capacitance of [tex]\( C_1 \)[/tex] is [tex]\( 25 \: \mu F \)[/tex] and the voltage provided by the battery is [tex]\( 7.5 \: V \)[/tex].

We use the fundamental formula for the charge on a capacitor:
[tex]\[ Q = C \cdot V \][/tex]

Here, [tex]\( Q \)[/tex] is the charge on the capacitor, [tex]\( C \)[/tex] is the capacitance, and [tex]\( V \)[/tex] is the voltage across the capacitor.

Since the capacitors are connected in parallel, each capacitor experiences the full voltage provided by the battery. Therefore, the voltage [tex]\( V \)[/tex] across capacitor [tex]\( C_1 \)[/tex] is [tex]\( 7.5 \: V \)[/tex].

We substitute the given values into the formula:
[tex]\[ Q_1 = C_1 \cdot V \][/tex]
[tex]\[ Q_1 = 25 \: \mu F \cdot 7.5 \: V \][/tex]

Multiplying these together gives:
[tex]\[ Q_1 = 187.5 \: \mu C \][/tex]

So, the charge [tex]\( Q_1 \)[/tex] on capacitor [tex]\( C_1 \)[/tex] is [tex]\( 187.5 \: \mu C \)[/tex].
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.