In Fig. 25-30, the battery has a potential difference of V = 10.0 V, and the five capacitors each have a capacitance of What is the charge on (a) capacitor 1 and (b) capacitor 2?
a) The charge on the capacitor
b) The charge on the capacitor
The potential difference is V = 10 V
Find the charge on capacitor 1 by using the concept of capacitance. To find the charge on capacitor 2, find the equivalent capacitance and potential difference across capacitors 2.
Formulae are as follows:
q = CV
For parallel combination,
For series combination,
Where C is capacitance, V is the potential difference, and q is the charge on the capacitor.
It is known that,
q = CV
The potential difference across the capacitor is,
So the charge on the capacitor 1 is,
Hence, the charge on the capacitor 1 is
For finding the charge , first, find the equivalent capacitance.
Consider the three-capacitor combination consisting of and its two closest neighbors, each of capacitance C. Using the formula for parallel and series combination of the capacitor, write the equivalent capacitance of this combination as
By substituting the values,
The voltage drop in this combination is,
By outing the value of ,
This voltage difference is divided into two equal parts between and the capacitor connected in series with it. So, the total voltage across the capacitor 2 is,
Thus, the total charge on the capacitor 2 will be,
By substituting the value of ,
Hence, the charge on the capacitor 2 is
Therefore, we can find the charge on both capacitors by using the concept of capacitance.
A potential difference of 300 V is applied to a series connection of two capacitors of capacitances and .What are (a) charge and (b) potential difference on capacitor 1 and (c) and (d) on capacitor 2? The charged capacitors are then disconnected from each other and from the battery. Then the capacitors are reconnected with plates of the same signs wired together (the battery is not used). What now are (e) , (f) , (g) , and (h) ? Suppose, instead, the capacitors charged in part (a) are reconnected with plates of opposite signs wired together. What now are (i) , ( j) , (k) , and (l) ?
A certain parallel plate capacitor is filled with a dielectric for which k = 5.5 . The area of each plate is , and the plates are separated by 2.0 mm .The capacitor will fail (short out and burn up) if the electric field between the plates exceeds . What is the maximum energy that can be stored in the capacitor?
Initially, a single capacitance is wired to a battery. Then capacitance is added in parallel. Are (a) the potential difference across and (b) the charge on now more than, less than, or the same as previously? (c) Is the equivalent capacitance of and more than, less than, or equal to ? (d) Is the charge stored on and C2 together more than, less than, or equal to the charge stored previously on ?
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