Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.